Prelude

Copyright (c) The University of Glasgow 2001
License BSD-style (see the file libraries/base/LICENSE)
Maintainer libraries@haskell.org
Stability stable
Portability portable
Safe Haskell Trustworthy
Language Haskell2010

Description

The Prelude: a standard module. The Prelude is imported by default into all Haskell modules unless either there is an explicit import statement for it, or the NoImplicitPrelude extension is enabled.

Standard types, classes and related functions

Basic data types

data Bool Source

Constructors

False
True
Instances
Instances details
Bits Bool Source

Interpret Bool as 1-bit bit-field

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Bits

FiniteBits Bool Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Bits

Data Bool Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Bool -> c Bool Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Bool Source

toConstr :: Bool -> Constr Source

dataTypeOf :: Bool -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Bool) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Bool) Source

gmapT :: (forall b. Data b => b -> b) -> Bool -> Bool Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Bool -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Bool -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source

Bounded Bool Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Enum Bool Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Storable Bool Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Foreign.Storable

Generic Bool Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep Bool

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep Bool = D1 ('MetaData "Bool" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "False" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "True" 'PrefixI 'False) (U1 :: Type -> Type))

Methods

from :: Bool -> Rep Bool x Source

to :: Rep Bool x -> Bool Source

SingKind Bool

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Associated Types

type DemoteRep Bool
Instance details

Defined in GHC.Internal.Generics

type DemoteRep Bool = Bool

Methods

fromSing :: forall (a :: Bool). Sing a -> DemoteRep Bool

Ix Bool Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Ix

Read Bool Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Show Bool Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Eq Bool Source
Instance details

Defined in GHC.Classes

Methods

(==) :: Bool -> Bool -> Bool Source

(/=) :: Bool -> Bool -> Bool Source

Ord Bool Source
Instance details

Defined in GHC.Classes

Methods

compare :: Bool -> Bool -> Ordering Source

(<) :: Bool -> Bool -> Bool Source

(<=) :: Bool -> Bool -> Bool Source

(>) :: Bool -> Bool -> Bool Source

(>=) :: Bool -> Bool -> Bool Source

max :: Bool -> Bool -> Bool Source

min :: Bool -> Bool -> Bool Source

SingI 'False

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

sing :: Sing 'False

SingI 'True

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

sing :: Sing 'True

Lift Bool Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Bool -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Bool -> Code m Bool Source

type DemoteRep Bool Source
Instance details

Defined in GHC.Internal.Generics

type DemoteRep Bool = Bool
type Rep Bool Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep Bool = D1 ('MetaData "Bool" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "False" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "True" 'PrefixI 'False) (U1 :: Type -> Type))
data Sing (a :: Bool) Source
Instance details

Defined in GHC.Internal.Generics

data Sing (a :: Bool) where

(&&) :: Bool -> Bool -> Bool infixr 3 Source

Boolean "and", lazy in the second argument

(||) :: Bool -> Bool -> Bool infixr 2 Source

Boolean "or", lazy in the second argument

not :: Bool -> Bool Source

Boolean "not"

otherwise :: Bool Source

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

data Maybe a Source

The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error.

The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Either type.

Constructors

Nothing
Just a
Instances
Instances details
Eq1 Maybe Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> Maybe a -> Maybe b -> Bool Source

Ord1 Maybe Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> Maybe a -> Maybe b -> Ordering Source

Read1 Maybe Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Maybe a) Source

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Maybe a] Source

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Maybe a) Source

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Maybe a] Source

Show1 Maybe Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Maybe a -> ShowS Source

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Maybe a] -> ShowS Source

Alternative Maybe Source

Picks the leftmost Just value, or, alternatively, Nothing.

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

empty :: Maybe a Source

(<|>) :: Maybe a -> Maybe a -> Maybe a Source

some :: Maybe a -> Maybe [a] Source

many :: Maybe a -> Maybe [a] Source

Applicative Maybe Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> Maybe a Source

(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source

liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source

(*>) :: Maybe a -> Maybe b -> Maybe b Source

(<*) :: Maybe a -> Maybe b -> Maybe a Source

Functor Maybe Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b Source

(<$) :: a -> Maybe b -> Maybe a Source

Monad Maybe Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source

(>>) :: Maybe a -> Maybe b -> Maybe b Source

return :: a -> Maybe a Source

MonadPlus Maybe Source

Picks the leftmost Just value, or, alternatively, Nothing.

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mzero :: Maybe a Source

mplus :: Maybe a -> Maybe a -> Maybe a Source

MonadFail Maybe Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fail

Methods

fail :: String -> Maybe a Source

MonadFix Maybe Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Control.Monad.Fix

Methods

mfix :: (a -> Maybe a) -> Maybe a Source

MonadZip Maybe Source

Since: ghc-internal-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Zip

Methods

mzip :: Maybe a -> Maybe b -> Maybe (a, b) Source

mzipWith :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source

munzip :: Maybe (a, b) -> (Maybe a, Maybe b) Source

Foldable Maybe Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Maybe m -> m Source

foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source

foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source

foldr :: (a -> b -> b) -> b -> Maybe a -> b Source

foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source

foldl :: (b -> a -> b) -> b -> Maybe a -> b Source

foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source

foldr1 :: (a -> a -> a) -> Maybe a -> a Source

foldl1 :: (a -> a -> a) -> Maybe a -> a Source

toList :: Maybe a -> [a] Source

null :: Maybe a -> Bool Source

length :: Maybe a -> Int Source

elem :: Eq a => a -> Maybe a -> Bool Source

maximum :: Ord a => Maybe a -> a Source

minimum :: Ord a => Maybe a -> a Source

sum :: Num a => Maybe a -> a Source

product :: Num a => Maybe a -> a Source

Traversable Maybe Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) Source

sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) Source

mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) Source

sequence :: Monad m => Maybe (m a) -> m (Maybe a) Source

Generic1 Maybe Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 Maybe

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 Maybe = D1 ('MetaData "Maybe" "GHC.Internal.Maybe" "ghc-internal" 'False) (C1 ('MetaCons "Nothing" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Just" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Maybe a -> Rep1 Maybe a Source

to1 :: Rep1 Maybe a -> Maybe a Source

Lift a => Lift (Maybe a :: Type) Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Maybe a -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Maybe a -> Code m (Maybe a) Source

Semigroup a => Monoid (Maybe a) Source

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S."

Since 4.11.0: constraint on inner a value generalised from Monoid to Semigroup.

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: Maybe a Source

mappend :: Maybe a -> Maybe a -> Maybe a Source

mconcat :: [Maybe a] -> Maybe a Source

Semigroup a => Semigroup (Maybe a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a Source

sconcat :: NonEmpty (Maybe a) -> Maybe a Source

stimes :: Integral b => b -> Maybe a -> Maybe a Source

Data a => Data (Maybe a) Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Maybe a -> c (Maybe a) Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Maybe a) Source

toConstr :: Maybe a -> Constr Source

dataTypeOf :: Maybe a -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Maybe a)) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Maybe a)) Source

gmapT :: (forall b. Data b => b -> b) -> Maybe a -> Maybe a Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Maybe a -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Maybe a -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source

Generic (Maybe a) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (Maybe a)

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (Maybe a) = D1 ('MetaData "Maybe" "GHC.Internal.Maybe" "ghc-internal" 'False) (C1 ('MetaCons "Nothing" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Just" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Maybe a -> Rep (Maybe a) x Source

to :: Rep (Maybe a) x -> Maybe a Source

SingKind a => SingKind (Maybe a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Associated Types

type DemoteRep (Maybe a)
Instance details

Defined in GHC.Internal.Generics

type DemoteRep (Maybe a) = Maybe (DemoteRep a)

Methods

fromSing :: forall (a0 :: Maybe a). Sing a0 -> DemoteRep (Maybe a)

Read a => Read (Maybe a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Show a => Show (Maybe a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> Maybe a -> ShowS Source

show :: Maybe a -> String Source

showList :: [Maybe a] -> ShowS Source

Eq a => Eq (Maybe a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Maybe

Methods

(==) :: Maybe a -> Maybe a -> Bool Source

(/=) :: Maybe a -> Maybe a -> Bool Source

Ord a => Ord (Maybe a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Maybe

Methods

compare :: Maybe a -> Maybe a -> Ordering Source

(<) :: Maybe a -> Maybe a -> Bool Source

(<=) :: Maybe a -> Maybe a -> Bool Source

(>) :: Maybe a -> Maybe a -> Bool Source

(>=) :: Maybe a -> Maybe a -> Bool Source

max :: Maybe a -> Maybe a -> Maybe a Source

min :: Maybe a -> Maybe a -> Maybe a Source

SingI ('Nothing :: Maybe a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

sing :: Sing ('Nothing :: Maybe a)

SingI a2 => SingI ('Just a2 :: Maybe a1)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

sing :: Sing ('Just a2)

type Rep1 Maybe Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 Maybe = D1 ('MetaData "Maybe" "GHC.Internal.Maybe" "ghc-internal" 'False) (C1 ('MetaCons "Nothing" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Just" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type DemoteRep (Maybe a) Source
Instance details

Defined in GHC.Internal.Generics

type DemoteRep (Maybe a) = Maybe (DemoteRep a)
type Rep (Maybe a) Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (Maybe a) = D1 ('MetaData "Maybe" "GHC.Internal.Maybe" "ghc-internal" 'False) (C1 ('MetaCons "Nothing" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Just" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
data Sing (b :: Maybe a) Source
Instance details

Defined in GHC.Internal.Generics

data Sing (b :: Maybe a) where

maybe :: b -> (a -> b) -> Maybe a -> b Source

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.

Examples
Expand

Basic usage:

>>> maybe False odd (Just 3)
True
>>> maybe False odd Nothing
False

Read an integer from a string using readMaybe. If we succeed, return twice the integer; that is, apply (*2) to it. If instead we fail to parse an integer, return 0 by default:

>>> import GHC.Internal.Text.Read ( readMaybe )
>>> maybe 0 (*2) (readMaybe "5")
10
>>> maybe 0 (*2) (readMaybe "")
0

Apply show to a Maybe Int. If we have Just n, we want to show the underlying Int n. But if we have Nothing, we return the empty string instead of (for example) "Nothing":

>>> maybe "" show (Just 5)
"5"
>>> maybe "" show Nothing
""

data Either a b Source

The Either type represents values with two possibilities: a value of type Either a b is either Left a or Right b.

The Either type is sometimes used to represent a value which is either correct or an error; by convention, the Left constructor is used to hold an error value and the Right constructor is used to hold a correct value (mnemonic: "right" also means "correct").

Examples
Expand

The type Either String Int is the type of values which can be either a String or an Int. The Left constructor can be used only on Strings, and the Right constructor can be used only on Ints:

>>> let s = Left "foo" :: Either String Int
>>> s
Left "foo"
>>> let n = Right 3 :: Either String Int
>>> n
Right 3
>>> :type s
s :: Either String Int
>>> :type n
n :: Either String Int

The fmap from our Functor instance will ignore Left values, but will apply the supplied function to values contained in a Right:

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> fmap (*2) s
Left "foo"
>>> fmap (*2) n
Right 6

The Monad instance for Either allows us to chain together multiple actions which may fail, and fail overall if any of the individual steps failed. First we'll write a function that can either parse an Int from a Char, or fail.

>>> import Data.Char ( digitToInt, isDigit )
>>> :{
    let parseEither :: Char -> Either String Int
        parseEither c
          | isDigit c = Right (digitToInt c)
          | otherwise = Left "parse error"
>>> :}

The following should work, since both '1' and '2' can be parsed as Ints.

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither '1'
          y <- parseEither '2'
          return (x + y)
>>> :}
>>> parseMultiple
Right 3

But the following should fail overall, since the first operation where we attempt to parse 'm' as an Int will fail:

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither 'm'
          y <- parseEither '2'
          return (x + y)
>>> :}
>>> parseMultiple
Left "parse error"

Constructors

Left a
Right b
Instances
Instances details
Bifoldable Either Source

Since: base-4.10.0.0

Instance details

Defined in Data.Bifoldable

Methods

bifold :: Monoid m => Either m m -> m Source

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Either a b -> m Source

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Either a b -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Either a b -> c Source

Bifoldable1 Either Source
Instance details

Defined in Data.Bifoldable1

Methods

bifold1 :: Semigroup m => Either m m -> m Source

bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Either a b -> m Source

Bifunctor Either Source

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d Source

first :: (a -> b) -> Either a c -> Either b c Source

second :: (b -> c) -> Either a b -> Either a c Source

Bitraversable Either Source

Since: base-4.10.0.0

Instance details

Defined in Data.Bitraversable

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) Source

Eq2 Either Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Either a c -> Either b d -> Bool Source

Ord2 Either Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Either a c -> Either b d -> Ordering Source

Read2 Either Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Either a b) Source

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Either a b] Source

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Either a b) Source

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Either a b] Source

Show2 Either Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Either a b -> ShowS Source

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Either a b] -> ShowS Source

Generic1 (Either a :: Type -> Type) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 (Either a :: Type -> Type)

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (Either a :: Type -> Type) = D1 ('MetaData "Either" "GHC.Internal.Data.Either" "ghc-internal" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Either a a0 -> Rep1 (Either a) a0 Source

to1 :: Rep1 (Either a) a0 -> Either a a0 Source

(Lift a, Lift b) => Lift (Either a b :: Type) Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Either a b -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Either a b -> Code m (Either a b) Source

Eq a => Eq1 (Either a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a0 -> b -> Bool) -> Either a a0 -> Either a b -> Bool Source

Ord a => Ord1 (Either a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a0 -> b -> Ordering) -> Either a a0 -> Either a b -> Ordering Source

Read a => Read1 (Either a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Either a a0) Source

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Either a a0] Source

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Either a a0) Source

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Either a a0] Source

Show a => Show1 (Either a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Either a a0 -> ShowS Source

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Either a a0] -> ShowS Source

Applicative (Either e) Source

Since: base-3.0

Instance details

Defined in GHC.Internal.Data.Either

Methods

pure :: a -> Either e a Source

(<*>) :: Either e (a -> b) -> Either e a -> Either e b Source

liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source

(*>) :: Either e a -> Either e b -> Either e b Source

(<*) :: Either e a -> Either e b -> Either e a Source

Functor (Either a) Source

Since: base-3.0

Instance details

Defined in GHC.Internal.Data.Either

Methods

fmap :: (a0 -> b) -> Either a a0 -> Either a b Source

(<$) :: a0 -> Either a b -> Either a a0 Source

Monad (Either e) Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Data.Either

Methods

(>>=) :: Either e a -> (a -> Either e b) -> Either e b Source

(>>) :: Either e a -> Either e b -> Either e b Source

return :: a -> Either e a Source

MonadFix (Either e) Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fix

Methods

mfix :: (a -> Either e a) -> Either e a Source

Foldable (Either a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Either a m -> m Source

foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source

foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source

foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source

foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source

foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source

foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source

foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source

foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source

toList :: Either a a0 -> [a0] Source

null :: Either a a0 -> Bool Source

length :: Either a a0 -> Int Source

elem :: Eq a0 => a0 -> Either a a0 -> Bool Source

maximum :: Ord a0 => Either a a0 -> a0 Source

minimum :: Ord a0 => Either a a0 -> a0 Source

sum :: Num a0 => Either a a0 -> a0 Source

product :: Num a0 => Either a a0 -> a0 Source

Traversable (Either a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) Source

sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) Source

mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) Source

sequence :: Monad m => Either a (m a0) -> m (Either a a0) Source

Semigroup (Either a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Either

Methods

(<>) :: Either a b -> Either a b -> Either a b Source

sconcat :: NonEmpty (Either a b) -> Either a b Source

stimes :: Integral b0 => b0 -> Either a b -> Either a b Source

(Data a, Data b) => Data (Either a b) Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Either a b -> c (Either a b) Source

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Either a b) Source

toConstr :: Either a b -> Constr Source

dataTypeOf :: Either a b -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Either a b)) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Either a b)) Source

gmapT :: (forall b0. Data b0 => b0 -> b0) -> Either a b -> Either a b Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Either a b -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Either a b -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source

Generic (Either a b) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (Either a b)

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (Either a b) = D1 ('MetaData "Either" "GHC.Internal.Data.Either" "ghc-internal" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b)))

Methods

from :: Either a b -> Rep (Either a b) x Source

to :: Rep (Either a b) x -> Either a b Source

(Read a, Read b) => Read (Either a b) Source

Since: base-3.0

Instance details

Defined in GHC.Internal.Data.Either

(Show a, Show b) => Show (Either a b) Source

Since: base-3.0

Instance details

Defined in GHC.Internal.Data.Either

Methods

showsPrec :: Int -> Either a b -> ShowS Source

show :: Either a b -> String Source

showList :: [Either a b] -> ShowS Source

(Eq a, Eq b) => Eq (Either a b) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Either

Methods

(==) :: Either a b -> Either a b -> Bool Source

(/=) :: Either a b -> Either a b -> Bool Source

(Ord a, Ord b) => Ord (Either a b) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Either

Methods

compare :: Either a b -> Either a b -> Ordering Source

(<) :: Either a b -> Either a b -> Bool Source

(<=) :: Either a b -> Either a b -> Bool Source

(>) :: Either a b -> Either a b -> Bool Source

(>=) :: Either a b -> Either a b -> Bool Source

max :: Either a b -> Either a b -> Either a b Source

min :: Either a b -> Either a b -> Either a b Source

type Rep1 (Either a :: Type -> Type) Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (Either a :: Type -> Type) = D1 ('MetaData "Either" "GHC.Internal.Data.Either" "ghc-internal" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Either a b) Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (Either a b) = D1 ('MetaData "Either" "GHC.Internal.Data.Either" "ghc-internal" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b)))

either :: (a -> c) -> (b -> c) -> Either a b -> c Source

Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.

Examples
Expand

We create two values of type Either String Int, one using the Left constructor and another using the Right constructor. Then we apply "either" the length function (if we have a String) or the "times-two" function (if we have an Int):

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> either length (*2) s
3
>>> either length (*2) n
6

data Ordering Source

Constructors

LT
EQ
GT
Instances
Instances details
Monoid Ordering Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Semigroup Ordering Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Data Ordering Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ordering -> c Ordering Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Ordering Source

toConstr :: Ordering -> Constr Source

dataTypeOf :: Ordering -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Ordering) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Ordering) Source

gmapT :: (forall b. Data b => b -> b) -> Ordering -> Ordering Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Ordering -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Ordering -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source

Bounded Ordering Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Enum Ordering Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Generic Ordering Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep Ordering

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep Ordering = D1 ('MetaData "Ordering" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "LT" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "EQ" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "GT" 'PrefixI 'False) (U1 :: Type -> Type)))
Ix Ordering Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Ix

Read Ordering Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Show Ordering Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Eq Ordering Source
Instance details

Defined in GHC.Classes

Ord Ordering Source
Instance details

Defined in GHC.Classes

type Rep Ordering Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep Ordering = D1 ('MetaData "Ordering" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "LT" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "EQ" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "GT" 'PrefixI 'False) (U1 :: Type -> Type)))

data Char Source

The character type Char represents Unicode codespace and its elements are code points as in definitions D9 and D10 of the Unicode Standard.

Character literals in Haskell are single-quoted: 'Q', 'Я' or 'Ω'. To represent a single quote itself use '\'', and to represent a backslash use '\\'. The full grammar can be found in the section 2.6 of the Haskell 2010 Language Report.

To specify a character by its code point one can use decimal, hexadecimal or octal notation: '\65', '\x41' and '\o101' are all alternative forms of 'A'. The largest code point is '\x10ffff'.

There is a special escape syntax for ASCII control characters:

Escape Alternatives Meaning
'\NUL' '\0' null character
'\SOH' '\1' start of heading
'\STX' '\2' start of text
'\ETX' '\3' end of text
'\EOT' '\4' end of transmission
'\ENQ' '\5' enquiry
'\ACK' '\6' acknowledge
'\BEL' '\7', '\a' bell (alert)
'\BS' '\8', '\b' backspace
'\HT' '\9', '\t' horizontal tab
'\LF' '\10', '\n' line feed (new line)
'\VT' '\11', '\v' vertical tab
'\FF' '\12', '\f' form feed
'\CR' '\13', '\r' carriage return
'\SO' '\14' shift out
'\SI' '\15' shift in
'\DLE' '\16' data link escape
'\DC1' '\17' device control 1
'\DC2' '\18' device control 2
'\DC3' '\19' device control 3
'\DC4' '\20' device control 4
'\NAK' '\21' negative acknowledge
'\SYN' '\22' synchronous idle
'\ETB' '\23' end of transmission block
'\CAN' '\24' cancel
'\EM' '\25' end of medium
'\SUB' '\26' substitute
'\ESC' '\27' escape
'\FS' '\28' file separator
'\GS' '\29' group separator
'\RS' '\30' record separator
'\US' '\31' unit separator
'\SP' '\32', ' ' space
'\DEL' '\127' delete

Data.Char provides utilities to work with Char.

Instances
Instances details
IsChar Char Source

Since: base-2.1

Instance details

Defined in Text.Printf

Methods

toChar :: Char -> Char Source

fromChar :: Char -> Char Source

PrintfArg Char Source

Since: base-2.1

Instance details

Defined in Text.Printf

Data Char Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Char -> c Char Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Char Source

toConstr :: Char -> Constr Source

dataTypeOf :: Char -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Char) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Char) Source

gmapT :: (forall b. Data b => b -> b) -> Char -> Char Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Char -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Char -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Char -> m Char Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char Source

Bounded Char Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Enum Char Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Storable Char Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Foreign.Storable

Ix Char Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Ix

Read Char Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Show Char Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Eq Char Source
Instance details

Defined in GHC.Classes

Methods

(==) :: Char -> Char -> Bool Source

(/=) :: Char -> Char -> Bool Source

Ord Char Source
Instance details

Defined in GHC.Classes

Methods

compare :: Char -> Char -> Ordering Source

(<) :: Char -> Char -> Bool Source

(<=) :: Char -> Char -> Bool Source

(>) :: Char -> Char -> Bool Source

(>=) :: Char -> Char -> Bool Source

max :: Char -> Char -> Char Source

min :: Char -> Char -> Char Source

TestCoercion SChar Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.TypeLits

Methods

testCoercion :: forall (a :: Char) (b :: Char). SChar a -> SChar b -> Maybe (Coercion a b) Source

TestEquality SChar Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.TypeLits

Methods

testEquality :: forall (a :: Char) (b :: Char). SChar a -> SChar b -> Maybe (a :~: b) Source

Lift Char Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Char -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Char -> Code m Char Source

Generic1 (URec Char :: k -> Type) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 (URec Char :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Char :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UChar" 'PrefixI 'True) (S1 ('MetaSel ('Just "uChar#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UChar :: k -> Type)))

Methods

from1 :: forall (a :: k). URec Char a -> Rep1 (URec Char :: k -> Type) a Source

to1 :: forall (a :: k). Rep1 (URec Char :: k -> Type) a -> URec Char a Source

Eq1 (UChar :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> UChar a -> UChar b -> Bool Source

Ord1 (UChar :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> UChar a -> UChar b -> Ordering Source

Show1 (UChar :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> UChar a -> ShowS Source

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [UChar a] -> ShowS Source

Foldable (UChar :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UChar m -> m Source

foldMap :: Monoid m => (a -> m) -> UChar a -> m Source

foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source

foldr :: (a -> b -> b) -> b -> UChar a -> b Source

foldr' :: (a -> b -> b) -> b -> UChar a -> b Source

foldl :: (b -> a -> b) -> b -> UChar a -> b Source

foldl' :: (b -> a -> b) -> b -> UChar a -> b Source

foldr1 :: (a -> a -> a) -> UChar a -> a Source

foldl1 :: (a -> a -> a) -> UChar a -> a Source

toList :: UChar a -> [a] Source

null :: UChar a -> Bool Source

length :: UChar a -> Int Source

elem :: Eq a => a -> UChar a -> Bool Source

maximum :: Ord a => UChar a -> a Source

minimum :: Ord a => UChar a -> a Source

sum :: Num a => UChar a -> a Source

product :: Num a => UChar a -> a Source

Traversable (UChar :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UChar a -> f (UChar b) Source

sequenceA :: Applicative f => UChar (f a) -> f (UChar a) Source

mapM :: Monad m => (a -> m b) -> UChar a -> m (UChar b) Source

sequence :: Monad m => UChar (m a) -> m (UChar a) Source

Functor (URec Char :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Char a -> URec Char b Source

(<$) :: a -> URec Char b -> URec Char a Source

Generic (URec Char p) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (URec Char p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (URec Char p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UChar" 'PrefixI 'True) (S1 ('MetaSel ('Just "uChar#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UChar :: Type -> Type)))

Methods

from :: URec Char p -> Rep (URec Char p) x Source

to :: Rep (URec Char p) x -> URec Char p Source

Show (URec Char p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Eq (URec Char p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Char p -> URec Char p -> Bool Source

(/=) :: URec Char p -> URec Char p -> Bool Source

Ord (URec Char p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: URec Char p -> URec Char p -> Ordering Source

(<) :: URec Char p -> URec Char p -> Bool Source

(<=) :: URec Char p -> URec Char p -> Bool Source

(>) :: URec Char p -> URec Char p -> Bool Source

(>=) :: URec Char p -> URec Char p -> Bool Source

max :: URec Char p -> URec Char p -> URec Char p Source

min :: URec Char p -> URec Char p -> URec Char p Source

data URec Char (p :: k) Source

Used for marking occurrences of Char#

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

data URec Char (p :: k) = UChar {}
type Compare (a :: Char) (b :: Char) Source
Instance details

Defined in GHC.Internal.Data.Type.Ord

type Compare (a :: Char) (b :: Char) = CmpChar a b
type Rep1 (URec Char :: k -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Char :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UChar" 'PrefixI 'True) (S1 ('MetaSel ('Just "uChar#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UChar :: k -> Type)))
type Rep (URec Char p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (URec Char p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UChar" 'PrefixI 'True) (S1 ('MetaSel ('Just "uChar#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UChar :: Type -> Type)))

type String = [Char] Source

String is an alias for a list of characters.

String constants in Haskell are values of type String. That means if you write a string literal like "hello world", it will have the type [Char], which is the same as String.

Note: You can ask the compiler to automatically infer different types with the -XOverloadedStrings language extension, for example "hello world" :: Text. See IsString for more information.

Because String is just a list of characters, you can use normal list functions to do basic string manipulation. See Data.List for operations on lists.

Performance considerations

Expand

[Char] is a relatively memory-inefficient type. It is a linked list of boxed word-size characters, internally it looks something like:

╭─────┬───┬──╮  ╭─────┬───┬──╮  ╭─────┬───┬──╮  ╭────╮
│ (:) │   │ ─┼─>│ (:) │   │ ─┼─>│ (:) │   │ ─┼─>│ [] │
╰─────┴─┼─┴──╯  ╰─────┴─┼─┴──╯  ╰─────┴─┼─┴──╯  ╰────╯
        v               v               v
       'a'             'b'             'c'

The String "abc" will use 5*3+1 = 16 (in general 5n+1) words of space in memory.

Furthermore, operations like (++) (string concatenation) are O(n) (in the left argument).

For historical reasons, the base library uses String in a lot of places for the conceptual simplicity, but library code dealing with user-data should use the text package for Unicode text, or the the bytestring package for binary data.

Tuples

fst :: (a, b) -> a Source

Extract the first component of a pair.

snd :: (a, b) -> b Source

Extract the second component of a pair.

curry :: ((a, b) -> c) -> a -> b -> c Source

Convert an uncurried function to a curried function.

Examples
Expand
>>> curry fst 1 2
1

uncurry :: (a -> b -> c) -> (a, b) -> c Source

uncurry converts a curried function to a function on pairs.

Examples
Expand
>>> uncurry (+) (1,2)
3
>>> uncurry ($) (show, 1)
"1"
>>> map (uncurry max) [(1,2), (3,4), (6,8)]
[2,4,8]

Basic type classes

class Eq a where Source

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq.

The Haskell Report defines no laws for Eq. However, instances are encouraged to follow these properties:

Reflexivity
x == x = True
Symmetry
x == y = y == x
Transitivity
if x == y && y == z = True, then x == z = True
Extensionality
if x == y = True and f is a function whose return type is an instance of Eq, then f x == f y = True
Negation
x /= y = not (x == y)

Minimal complete definition

(==) | (/=)

Methods

(==) :: a -> a -> Bool infix 4 Source

(/=) :: a -> a -> Bool infix 4 Source

Instances
Instances details
Eq ByteArray Source

Since: base-4.17.0.0

Instance details

Defined in Data.Array.Byte

Eq Timeout Source
Instance details

Defined in System.Timeout

Eq BigNat
Instance details

Defined in GHC.Num.BigNat

Methods

(==) :: BigNat -> BigNat -> Bool Source

(/=) :: BigNat -> BigNat -> Bool Source

Eq Void Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(==) :: Void -> Void -> Bool Source

(/=) :: Void -> Void -> Bool Source

Eq ByteOrder Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.ByteOrder

Eq ClosureType Source
Instance details

Defined in GHC.Internal.ClosureTypes

Eq BlockReason Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Eq ThreadId Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Eq ThreadStatus Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Eq Constr Source

Equality of constructors

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

(==) :: Constr -> Constr -> Bool Source

(/=) :: Constr -> Constr -> Bool Source

Eq ConstrRep Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Eq DataRep Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Eq Fixity Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

(==) :: Fixity -> Fixity -> Bool Source

(/=) :: Fixity -> Fixity -> Bool Source

Eq All Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: All -> All -> Bool Source

(/=) :: All -> All -> Bool Source

Eq Any Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: Any -> Any -> Bool Source

(/=) :: Any -> Any -> Bool Source

Eq SomeTypeRep Source
Instance details

Defined in GHC.Internal.Data.Typeable.Internal

Eq Unique Source
Instance details

Defined in GHC.Internal.Data.Unique

Methods

(==) :: Unique -> Unique -> Bool Source

(/=) :: Unique -> Unique -> Bool Source

Eq Version Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Version

Eq ControlMessage Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Control

Methods

(==) :: ControlMessage -> ControlMessage -> Bool Source

(/=) :: ControlMessage -> ControlMessage -> Bool Source

Eq Event Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Methods

(==) :: Event -> Event -> Bool Source

(/=) :: Event -> Event -> Bool Source

Eq EventLifetime Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Methods

(==) :: EventLifetime -> EventLifetime -> Bool Source

(/=) :: EventLifetime -> EventLifetime -> Bool Source

Eq Lifetime Source

Since: base-4.8.1.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Eq FdKey Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Manager

Methods

(==) :: FdKey -> FdKey -> Bool Source

(/=) :: FdKey -> FdKey -> Bool Source

Eq State Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Manager

Methods

(==) :: State -> State -> Bool Source

(/=) :: State -> State -> Bool Source

Eq TimeoutKey Source
Instance details

Defined in GHC.Internal.Event.TimeOut

Eq State Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Event.TimerManager

Methods

(==) :: State -> State -> Bool Source

(/=) :: State -> State -> Bool Source

Eq Unique Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Unique

Methods

(==) :: Unique -> Unique -> Bool Source

(/=) :: Unique -> Unique -> Bool Source

Eq ErrorCall Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Exception

Eq ArithException Source

Since: base-3.0

Instance details

Defined in GHC.Internal.Exception.Type

Eq SpecConstrAnnotation Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.Exts

Eq Fingerprint Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Fingerprint.Type

Eq Errno Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Foreign.C.Error

Methods

(==) :: Errno -> Errno -> Bool Source

(/=) :: Errno -> Errno -> Bool Source

Eq CBool Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CBool -> CBool -> Bool Source

(/=) :: CBool -> CBool -> Bool Source

Eq CChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CChar -> CChar -> Bool Source

(/=) :: CChar -> CChar -> Bool Source

Eq CClock Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CClock -> CClock -> Bool Source

(/=) :: CClock -> CClock -> Bool Source

Eq CDouble Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Eq CFloat Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CFloat -> CFloat -> Bool Source

(/=) :: CFloat -> CFloat -> Bool Source

Eq CInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CInt -> CInt -> Bool Source

(/=) :: CInt -> CInt -> Bool Source

Eq CIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Eq CIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Eq CLLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CLLong -> CLLong -> Bool Source

(/=) :: CLLong -> CLLong -> Bool Source

Eq CLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CLong -> CLong -> Bool Source

(/=) :: CLong -> CLong -> Bool Source

Eq CPtrdiff Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Eq CSChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CSChar -> CSChar -> Bool Source

(/=) :: CSChar -> CSChar -> Bool Source

Eq CSUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Eq CShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CShort -> CShort -> Bool Source

(/=) :: CShort -> CShort -> Bool Source

Eq CSigAtomic Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Eq CSize Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CSize -> CSize -> Bool Source

(/=) :: CSize -> CSize -> Bool Source

Eq CTime Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CTime -> CTime -> Bool Source

(/=) :: CTime -> CTime -> Bool Source

Eq CUChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CUChar -> CUChar -> Bool Source

(/=) :: CUChar -> CUChar -> Bool Source

Eq CUInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CUInt -> CUInt -> Bool Source

(/=) :: CUInt -> CUInt -> Bool Source

Eq CUIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Eq CUIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Eq CULLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Eq CULong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CULong -> CULong -> Bool Source

(/=) :: CULong -> CULong -> Bool Source

Eq CUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Eq CUShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Eq CWchar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

(==) :: CWchar -> CWchar -> Bool Source

(/=) :: CWchar -> CWchar -> Bool Source

Eq IntPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Methods

(==) :: IntPtr -> IntPtr -> Bool Source

(/=) :: IntPtr -> IntPtr -> Bool Source

Eq WordPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Eq ForeignSrcLang Source
Instance details

Defined in GHC.Internal.ForeignSrcLang

Eq Associativity Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

Eq DecidedStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Eq Fixity Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: Fixity -> Fixity -> Bool Source

(/=) :: Fixity -> Fixity -> Bool Source

Eq SourceStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Eq SourceUnpackedness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Eq MaskingState Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.IO

Eq BufferState Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Buffer

Eq IODeviceType Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Device

Eq SeekMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Device

Eq CodingProgress Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.IO.Encoding.Types

Eq ArrayException Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Eq AsyncException Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Eq ExitCode Source
Instance details

Defined in GHC.Internal.IO.Exception

Eq IOErrorType Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Eq IOException Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Eq HandlePosn Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Handle

Eq BufferMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Eq Handle Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Methods

(==) :: Handle -> Handle -> Bool Source

(/=) :: Handle -> Handle -> Bool Source

Eq Newline Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Eq NewlineMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Eq IOMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.IOMode

Methods

(==) :: IOMode -> IOMode -> Bool Source

(/=) :: IOMode -> IOMode -> Bool Source

Eq IoSubSystem Source
Instance details

Defined in GHC.Internal.IO.SubSystem

Eq InfoProv Source
Instance details

Defined in GHC.Internal.InfoProv.Types

Eq Int16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Methods

(==) :: Int16 -> Int16 -> Bool Source

(/=) :: Int16 -> Int16 -> Bool Source

Eq Int32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Methods

(==) :: Int32 -> Int32 -> Bool Source

(/=) :: Int32 -> Int32 -> Bool Source

Eq Int64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Methods

(==) :: Int64 -> Int64 -> Bool Source

(/=) :: Int64 -> Int64 -> Bool Source

Eq Int8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Methods

(==) :: Int8 -> Int8 -> Bool Source

(/=) :: Int8 -> Int8 -> Bool Source

Eq Extension Source
Instance details

Defined in GHC.Internal.LanguageExtensions

Eq IoManagerFlag Source
Instance details

Defined in GHC.Internal.RTS.Flags

Eq StackEntry Source
Instance details

Defined in GHC.Internal.Stack.CloneStack

Eq SrcLoc Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Stack.Types

Methods

(==) :: SrcLoc -> SrcLoc -> Bool Source

(/=) :: SrcLoc -> SrcLoc -> Bool Source

Eq CBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Eq CBlkSize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Eq CCc Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CCc -> CCc -> Bool Source

(/=) :: CCc -> CCc -> Bool Source

Eq CClockId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Eq CDev Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CDev -> CDev -> Bool Source

(/=) :: CDev -> CDev -> Bool Source

Eq CFsBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Eq CFsFilCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Eq CGid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CGid -> CGid -> Bool Source

(/=) :: CGid -> CGid -> Bool Source

Eq CId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CId -> CId -> Bool Source

(/=) :: CId -> CId -> Bool Source

Eq CIno Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CIno -> CIno -> Bool Source

(/=) :: CIno -> CIno -> Bool Source

Eq CKey Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CKey -> CKey -> Bool Source

(/=) :: CKey -> CKey -> Bool Source

Eq CMode Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CMode -> CMode -> Bool Source

(/=) :: CMode -> CMode -> Bool Source

Eq CNfds Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CNfds -> CNfds -> Bool Source

(/=) :: CNfds -> CNfds -> Bool Source

Eq CNlink Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CNlink -> CNlink -> Bool Source

(/=) :: CNlink -> CNlink -> Bool Source

Eq COff Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: COff -> COff -> Bool Source

(/=) :: COff -> COff -> Bool Source

Eq CPid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CPid -> CPid -> Bool Source

(/=) :: CPid -> CPid -> Bool Source

Eq CRLim Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CRLim -> CRLim -> Bool Source

(/=) :: CRLim -> CRLim -> Bool Source

Eq CSocklen Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Eq CSpeed Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CSpeed -> CSpeed -> Bool Source

(/=) :: CSpeed -> CSpeed -> Bool Source

Eq CSsize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CSsize -> CSsize -> Bool Source

(/=) :: CSsize -> CSsize -> Bool Source

Eq CTcflag Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Eq CTimer Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CTimer -> CTimer -> Bool Source

(/=) :: CTimer -> CTimer -> Bool Source

Eq CUid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: CUid -> CUid -> Bool Source

(/=) :: CUid -> CUid -> Bool Source

Eq Fd Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(==) :: Fd -> Fd -> Bool Source

(/=) :: Fd -> Fd -> Bool Source

Eq AnnLookup Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq AnnTarget Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Bang Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Bang -> Bang -> Bool Source

(/=) :: Bang -> Bang -> Bool Source

Eq BndrVis Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Body Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Body -> Body -> Bool Source

(/=) :: Body -> Body -> Bool Source

Eq Bytes Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Bytes -> Bytes -> Bool Source

(/=) :: Bytes -> Bytes -> Bool Source

Eq Callconv Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Clause Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Clause -> Clause -> Bool Source

(/=) :: Clause -> Clause -> Bool Source

Eq Con Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Con -> Con -> Bool Source

(/=) :: Con -> Con -> Bool Source

Eq Dec Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Dec -> Dec -> Bool Source

(/=) :: Dec -> Dec -> Bool Source

Eq DecidedStrictness Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq DerivClause Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq DerivStrategy Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq DocLoc Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: DocLoc -> DocLoc -> Bool Source

(/=) :: DocLoc -> DocLoc -> Bool Source

Eq Exp Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Exp -> Exp -> Bool Source

(/=) :: Exp -> Exp -> Bool Source

Eq FamilyResultSig Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Fixity Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Fixity -> Fixity -> Bool Source

(/=) :: Fixity -> Fixity -> Bool Source

Eq FixityDirection Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Foreign Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq FunDep Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: FunDep -> FunDep -> Bool Source

(/=) :: FunDep -> FunDep -> Bool Source

Eq Guard Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Guard -> Guard -> Bool Source

(/=) :: Guard -> Guard -> Bool Source

Eq Info Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Info -> Info -> Bool Source

(/=) :: Info -> Info -> Bool Source

Eq InjectivityAnn Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Inline Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Inline -> Inline -> Bool Source

(/=) :: Inline -> Inline -> Bool Source

Eq Lit Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Lit -> Lit -> Bool Source

(/=) :: Lit -> Lit -> Bool Source

Eq Loc Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Loc -> Loc -> Bool Source

(/=) :: Loc -> Loc -> Bool Source

Eq Match Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Match -> Match -> Bool Source

(/=) :: Match -> Match -> Bool Source

Eq ModName Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Module Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Module -> Module -> Bool Source

(/=) :: Module -> Module -> Bool Source

Eq ModuleInfo Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Name Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Name -> Name -> Bool Source

(/=) :: Name -> Name -> Bool Source

Eq NameFlavour Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq NameSpace Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq NamespaceSpecifier Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq OccName Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Overlap Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Pat Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Pat -> Pat -> Bool Source

(/=) :: Pat -> Pat -> Bool Source

Eq PatSynArgs Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq PatSynDir Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Phases Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Phases -> Phases -> Bool Source

(/=) :: Phases -> Phases -> Bool Source

Eq PkgName Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Pragma Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Pragma -> Pragma -> Bool Source

(/=) :: Pragma -> Pragma -> Bool Source

Eq Range Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Range -> Range -> Bool Source

(/=) :: Range -> Range -> Bool Source

Eq Role Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Role -> Role -> Bool Source

(/=) :: Role -> Role -> Bool Source

Eq RuleBndr Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq RuleMatch Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Safety Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Safety -> Safety -> Bool Source

(/=) :: Safety -> Safety -> Bool Source

Eq SourceStrictness Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq SourceUnpackedness Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Specificity Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Stmt Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Stmt -> Stmt -> Bool Source

(/=) :: Stmt -> Stmt -> Bool Source

Eq TyLit Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: TyLit -> TyLit -> Bool Source

(/=) :: TyLit -> TyLit -> Bool Source

Eq TySynEqn Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Type Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: Type -> Type -> Bool Source

(/=) :: Type -> Type -> Bool Source

Eq TypeFamilyHead Source
Instance details

Defined in GHC.Internal.TH.Syntax

Eq Lexeme Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Text.Read.Lex

Methods

(==) :: Lexeme -> Lexeme -> Bool Source

(/=) :: Lexeme -> Lexeme -> Bool Source

Eq Number Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Text.Read.Lex

Methods

(==) :: Number -> Number -> Bool Source

(/=) :: Number -> Number -> Bool Source

Eq SomeChar Source
Instance details

Defined in GHC.Internal.TypeLits

Eq SomeSymbol Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.TypeLits

Eq SomeNat Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.TypeNats

Eq GeneralCategory Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Unicode

Eq Word16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Methods

(==) :: Word16 -> Word16 -> Bool Source

(/=) :: Word16 -> Word16 -> Bool Source

Eq Word32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Methods

(==) :: Word32 -> Word32 -> Bool Source

(/=) :: Word32 -> Word32 -> Bool Source

Eq Word64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Methods

(==) :: Word64 -> Word64 -> Bool Source

(/=) :: Word64 -> Word64 -> Bool Source

Eq Word8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Methods

(==) :: Word8 -> Word8 -> Bool Source

(/=) :: Word8 -> Word8 -> Bool Source

Eq Module Source
Instance details

Defined in GHC.Classes

Methods

(==) :: Module -> Module -> Bool Source

(/=) :: Module -> Module -> Bool Source

Eq Ordering Source
Instance details

Defined in GHC.Classes

Eq TrName Source
Instance details

Defined in GHC.Classes

Methods

(==) :: TrName -> TrName -> Bool Source

(/=) :: TrName -> TrName -> Bool Source

Eq TyCon Source
Instance details

Defined in GHC.Classes

Methods

(==) :: TyCon -> TyCon -> Bool Source

(/=) :: TyCon -> TyCon -> Bool Source

Eq Integer
Instance details

Defined in GHC.Num.Integer

Eq Natural
Instance details

Defined in GHC.Num.Natural

Eq () Source
Instance details

Defined in GHC.Classes

Methods

(==) :: () -> () -> Bool Source

(/=) :: () -> () -> Bool Source

Eq Bool Source
Instance details

Defined in GHC.Classes

Methods

(==) :: Bool -> Bool -> Bool Source

(/=) :: Bool -> Bool -> Bool Source

Eq Char Source
Instance details

Defined in GHC.Classes

Methods

(==) :: Char -> Char -> Bool Source

(/=) :: Char -> Char -> Bool Source

Eq Double Source

Note that due to the presence of NaN, Double's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Double)
False

Also note that Double's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Double)
True
>>> recip 0 == recip (-0 :: Double)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Double -> Double -> Bool Source

(/=) :: Double -> Double -> Bool Source

Eq Float Source

Note that due to the presence of NaN, Float's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Float)
False

Also note that Float's Eq instance does not satisfy extensionality:

>>> 0 == (-0 :: Float)
True
>>> recip 0 == recip (-0 :: Float)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Float -> Float -> Bool Source

(/=) :: Float -> Float -> Bool Source

Eq Int Source
Instance details

Defined in GHC.Classes

Methods

(==) :: Int -> Int -> Bool Source

(/=) :: Int -> Int -> Bool Source

Eq Word Source
Instance details

Defined in GHC.Classes

Methods

(==) :: Word -> Word -> Bool Source

(/=) :: Word -> Word -> Bool Source

Eq (Chan a) Source

Since: base-4.4.0.0

Instance details

Defined in Control.Concurrent.Chan

Methods

(==) :: Chan a -> Chan a -> Bool Source

(/=) :: Chan a -> Chan a -> Bool Source

Eq (MutableByteArray s) Source

Since: base-4.17.0.0

Instance details

Defined in Data.Array.Byte

Eq a => Eq (Complex a) Source

Since: base-2.1

Instance details

Defined in Data.Complex

Methods

(==) :: Complex a -> Complex a -> Bool Source

(/=) :: Complex a -> Complex a -> Bool Source

Eq a => Eq (First a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: First a -> First a -> Bool Source

(/=) :: First a -> First a -> Bool Source

Eq a => Eq (Last a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Last a -> Last a -> Bool Source

(/=) :: Last a -> Last a -> Bool Source

Eq a => Eq (Max a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Max a -> Max a -> Bool Source

(/=) :: Max a -> Max a -> Bool Source

Eq a => Eq (Min a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Min a -> Min a -> Bool Source

(/=) :: Min a -> Min a -> Bool Source

Eq m => Eq (WrappedMonoid m) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Eq a => Eq (NonEmpty a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(==) :: NonEmpty a -> NonEmpty a -> Bool Source

(/=) :: NonEmpty a -> NonEmpty a -> Bool Source

Eq (TVar a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Methods

(==) :: TVar a -> TVar a -> Bool Source

(/=) :: TVar a -> TVar a -> Bool Source

Eq a => Eq (And a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

(==) :: And a -> And a -> Bool Source

(/=) :: And a -> And a -> Bool Source

Eq a => Eq (Iff a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

(==) :: Iff a -> Iff a -> Bool Source

(/=) :: Iff a -> Iff a -> Bool Source

Eq a => Eq (Ior a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

(==) :: Ior a -> Ior a -> Bool Source

(/=) :: Ior a -> Ior a -> Bool Source

Eq a => Eq (Xor a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

(==) :: Xor a -> Xor a -> Bool Source

(/=) :: Xor a -> Xor a -> Bool Source

Eq a => Eq (Identity a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Methods

(==) :: Identity a -> Identity a -> Bool Source

(/=) :: Identity a -> Identity a -> Bool Source

Eq a => Eq (First a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(==) :: First a -> First a -> Bool Source

(/=) :: First a -> First a -> Bool Source

Eq a => Eq (Last a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(==) :: Last a -> Last a -> Bool Source

(/=) :: Last a -> Last a -> Bool Source

Eq a => Eq (Down a) Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

(==) :: Down a -> Down a -> Bool Source

(/=) :: Down a -> Down a -> Bool Source

Eq a => Eq (Dual a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: Dual a -> Dual a -> Bool Source

(/=) :: Dual a -> Dual a -> Bool Source

Eq a => Eq (Product a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: Product a -> Product a -> Bool Source

(/=) :: Product a -> Product a -> Bool Source

Eq a => Eq (Sum a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: Sum a -> Sum a -> Bool Source

(/=) :: Sum a -> Sum a -> Bool Source

Eq (ConstPtr a) Source
Instance details

Defined in GHC.Internal.Foreign.C.ConstPtr

Methods

(==) :: ConstPtr a -> ConstPtr a -> Bool Source

(/=) :: ConstPtr a -> ConstPtr a -> Bool Source

Eq (ForeignPtr a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.ForeignPtr

Eq a => Eq (ZipList a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

(==) :: ZipList a -> ZipList a -> Bool Source

(/=) :: ZipList a -> ZipList a -> Bool Source

Eq p => Eq (Par1 p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: Par1 p -> Par1 p -> Bool Source

(/=) :: Par1 p -> Par1 p -> Bool Source

Eq (IOPort a) Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IOPort

Methods

(==) :: IOPort a -> IOPort a -> Bool Source

(/=) :: IOPort a -> IOPort a -> Bool Source

Eq (IORef a) Source

Pointer equality.

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.IORef

Methods

(==) :: IORef a -> IORef a -> Bool Source

(/=) :: IORef a -> IORef a -> Bool Source

Eq (MVar a) Source

Compares the underlying pointers.

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.MVar

Methods

(==) :: MVar a -> MVar a -> Bool Source

(/=) :: MVar a -> MVar a -> Bool Source

Eq (FunPtr a) Source
Instance details

Defined in GHC.Internal.Ptr

Methods

(==) :: FunPtr a -> FunPtr a -> Bool Source

(/=) :: FunPtr a -> FunPtr a -> Bool Source

Eq (Ptr a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Ptr

Methods

(==) :: Ptr a -> Ptr a -> Bool Source

(/=) :: Ptr a -> Ptr a -> Bool Source

Eq a => Eq (Ratio a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Real

Methods

(==) :: Ratio a -> Ratio a -> Bool Source

(/=) :: Ratio a -> Ratio a -> Bool Source

Eq (StablePtr a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Stable

Methods

(==) :: StablePtr a -> StablePtr a -> Bool Source

(/=) :: StablePtr a -> StablePtr a -> Bool Source

Eq (StableName a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.StableName

Eq flag => Eq (TyVarBndr flag) Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(==) :: TyVarBndr flag -> TyVarBndr flag -> Bool Source

(/=) :: TyVarBndr flag -> TyVarBndr flag -> Bool Source

Eq (SChar c) Source

Since: base-4.19.0.0

Instance details

Defined in GHC.Internal.TypeLits

Methods

(==) :: SChar c -> SChar c -> Bool Source

(/=) :: SChar c -> SChar c -> Bool Source

Eq (SSymbol s) Source

Since: base-4.19.0.0

Instance details

Defined in GHC.Internal.TypeLits

Methods

(==) :: SSymbol s -> SSymbol s -> Bool Source

(/=) :: SSymbol s -> SSymbol s -> Bool Source

Eq (SNat n) Source

Since: base-4.19.0.0

Instance details

Defined in GHC.Internal.TypeNats

Methods

(==) :: SNat n -> SNat n -> Bool Source

(/=) :: SNat n -> SNat n -> Bool Source

Eq a => Eq (Maybe a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Maybe

Methods

(==) :: Maybe a -> Maybe a -> Bool Source

(/=) :: Maybe a -> Maybe a -> Bool Source

Eq a => Eq (Solo a) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: Solo a -> Solo a -> Bool Source

(/=) :: Solo a -> Solo a -> Bool Source

Eq a => Eq [a] Source
Instance details

Defined in GHC.Classes

Methods

(==) :: [a] -> [a] -> Bool Source

(/=) :: [a] -> [a] -> Bool Source

Eq (Fixed a) Source

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

(==) :: Fixed a -> Fixed a -> Bool Source

(/=) :: Fixed a -> Fixed a -> Bool Source

Eq a => Eq (Arg a b) Source

Note that Arg's Eq instance does not satisfy extensionality:

>>> Arg 0 0 == Arg 0 1
True
>>> let f (Arg _ x) = x in f (Arg 0 0) == f (Arg 0 1)
False

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Arg a b -> Arg a b -> Bool Source

(/=) :: Arg a b -> Arg a b -> Bool Source

(Ix i, Eq e) => Eq (Array i e) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Arr

Methods

(==) :: Array i e -> Array i e -> Bool Source

(/=) :: Array i e -> Array i e -> Bool Source

(Eq a, Eq b) => Eq (Either a b) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Either

Methods

(==) :: Either a b -> Either a b -> Bool Source

(/=) :: Either a b -> Either a b -> Bool Source

Eq (Proxy s) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

(==) :: Proxy s -> Proxy s -> Bool Source

(/=) :: Proxy s -> Proxy s -> Bool Source

Eq (TypeRep a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Typeable.Internal

Methods

(==) :: TypeRep a -> TypeRep a -> Bool Source

(/=) :: TypeRep a -> TypeRep a -> Bool Source

Eq (U1 p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: U1 p -> U1 p -> Bool Source

(/=) :: U1 p -> U1 p -> Bool Source

Eq (V1 p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: V1 p -> V1 p -> Bool Source

(/=) :: V1 p -> V1 p -> Bool Source

Eq (IOArray i e) Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IOArray

Methods

(==) :: IOArray i e -> IOArray i e -> Bool Source

(/=) :: IOArray i e -> IOArray i e -> Bool Source

Eq (STRef s a) Source

Pointer equality.

Since: base-2.1

Instance details

Defined in GHC.Internal.STRef

Methods

(==) :: STRef s a -> STRef s a -> Bool Source

(/=) :: STRef s a -> STRef s a -> Bool Source

(Eq a, Eq b) => Eq (a, b) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b) -> (a, b) -> Bool Source

(/=) :: (a, b) -> (a, b) -> Bool Source

Eq (STArray s i e) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Arr

Methods

(==) :: STArray s i e -> STArray s i e -> Bool Source

(/=) :: STArray s i e -> STArray s i e -> Bool Source

Eq a => Eq (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

(==) :: Const a b -> Const a b -> Bool Source

(/=) :: Const a b -> Const a b -> Bool Source

Eq (f a) => Eq (Ap f a) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(==) :: Ap f a -> Ap f a -> Bool Source

(/=) :: Ap f a -> Ap f a -> Bool Source

Eq (f a) => Eq (Alt f a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: Alt f a -> Alt f a -> Bool Source

(/=) :: Alt f a -> Alt f a -> Bool Source

Eq (Coercion a b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Coercion

Methods

(==) :: Coercion a b -> Coercion a b -> Bool Source

(/=) :: Coercion a b -> Coercion a b -> Bool Source

Eq (a :~: b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

Methods

(==) :: (a :~: b) -> (a :~: b) -> Bool Source

(/=) :: (a :~: b) -> (a :~: b) -> Bool Source

Eq (OrderingI a b) Source
Instance details

Defined in GHC.Internal.Data.Type.Ord

Methods

(==) :: OrderingI a b -> OrderingI a b -> Bool Source

(/=) :: OrderingI a b -> OrderingI a b -> Bool Source

(Generic1 f, Eq (Rep1 f a)) => Eq (Generically1 f a) Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: Generically1 f a -> Generically1 f a -> Bool Source

(/=) :: Generically1 f a -> Generically1 f a -> Bool Source

Eq (f p) => Eq (Rec1 f p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: Rec1 f p -> Rec1 f p -> Bool Source

(/=) :: Rec1 f p -> Rec1 f p -> Bool Source

Eq (URec (Ptr ()) p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source

(/=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source

Eq (URec Char p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Char p -> URec Char p -> Bool Source

(/=) :: URec Char p -> URec Char p -> Bool Source

Eq (URec Double p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Double p -> URec Double p -> Bool Source

(/=) :: URec Double p -> URec Double p -> Bool Source

Eq (URec Float p) Source
Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Float p -> URec Float p -> Bool Source

(/=) :: URec Float p -> URec Float p -> Bool Source

Eq (URec Int p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Int p -> URec Int p -> Bool Source

(/=) :: URec Int p -> URec Int p -> Bool Source

Eq (URec Word p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Word p -> URec Word p -> Bool Source

(/=) :: URec Word p -> URec Word p -> Bool Source

(Eq a, Eq b, Eq c) => Eq (a, b, c) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c) -> (a, b, c) -> Bool Source

(/=) :: (a, b, c) -> (a, b, c) -> Bool Source

(Eq (f a), Eq (g a)) => Eq (Product f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Product

Methods

(==) :: Product f g a -> Product f g a -> Bool Source

(/=) :: Product f g a -> Product f g a -> Bool Source

(Eq (f a), Eq (g a)) => Eq (Sum f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Sum

Methods

(==) :: Sum f g a -> Sum f g a -> Bool Source

(/=) :: Sum f g a -> Sum f g a -> Bool Source

Eq (a :~~: b) Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

Methods

(==) :: (a :~~: b) -> (a :~~: b) -> Bool Source

(/=) :: (a :~~: b) -> (a :~~: b) -> Bool Source

(Eq (f p), Eq (g p)) => Eq ((f :*: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: (f :*: g) p -> (f :*: g) p -> Bool Source

(/=) :: (f :*: g) p -> (f :*: g) p -> Bool Source

(Eq (f p), Eq (g p)) => Eq ((f :+: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: (f :+: g) p -> (f :+: g) p -> Bool Source

(/=) :: (f :+: g) p -> (f :+: g) p -> Bool Source

Eq c => Eq (K1 i c p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: K1 i c p -> K1 i c p -> Bool Source

(/=) :: K1 i c p -> K1 i c p -> Bool Source

(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source

(/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source

Eq (f (g a)) => Eq (Compose f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Compose

Methods

(==) :: Compose f g a -> Compose f g a -> Bool Source

(/=) :: Compose f g a -> Compose f g a -> Bool Source

Eq (f (g p)) => Eq ((f :.: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: (f :.: g) p -> (f :.: g) p -> Bool Source

(/=) :: (f :.: g) p -> (f :.: g) p -> Bool Source

Eq (f p) => Eq (M1 i c f p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: M1 i c f p -> M1 i c f p -> Bool Source

(/=) :: M1 i c f p -> M1 i c f p -> Bool Source

(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source

(/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source

(/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source

(/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source

(/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source

(/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source

(/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source

(/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source

class Eq a => Ord a where Source

The Ord class is used for totally ordered datatypes.

Instances of Ord can be derived for any user-defined datatype whose constituent types are in Ord. The declared order of the constructors in the data declaration determines the ordering in derived Ord instances. The Ordering datatype allows a single comparison to determine the precise ordering of two objects.

Ord, as defined by the Haskell report, implements a total order and has the following properties:

Comparability
x <= y || y <= x = True
Transitivity
if x <= y && y <= z = True, then x <= z = True
Reflexivity
x <= x = True
Antisymmetry
if x <= y && y <= x = True, then x == y = True

The following operator interactions are expected to hold:

  1. x >= y = y <= x
  2. x < y = x <= y && x /= y
  3. x > y = y < x
  4. x < y = compare x y == LT
  5. x > y = compare x y == GT
  6. x == y = compare x y == EQ
  7. min x y == if x <= y then x else y = True
  8. max x y == if x >= y then x else y = True

Note that (7.) and (8.) do not require min and max to return either of their arguments. The result is merely required to equal one of the arguments in terms of (==). Users who expect a stronger guarantee are advised to write their own min and/or max functions.

The nuance of the above distinction is not always fully internalized by developers, and in the past (tracing back to the Haskell 1.4 Report) the specification for Ord asserted the stronger property that (min x y, max x y) = (x, y) or (y, x), or in other words, that min and max will return one of their arguments, using argument order as the tie-breaker if the arguments are equal by comparison. A few list and Foldable functions have behavior that is best understood with this assumption in mind: all variations of minimumBy and maximumBy (which can't use min and max in their implementations) are written such that minimumBy compare and maximumBy compare are respectively equivalent to minimum and maximum (which do use min and max) only if min and max adhere to this tie-breaking convention. Otherwise, if there are multiple least or largest elements in a container, minimum and maximum may not return the same one that minimumBy compare and maximumBy compare do (though they should return something that is equal). (This is relevant for types with non-extensional equality, like Arg, but also in cases where the precise reference held matters for memory-management reasons.) Unless there is a reason to deviate, it is less confusing for implementors of Ord to respect this same convention (as the default definitions of min and max do).

Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types.

Minimal complete definition

compare | (<=)

Methods

compare :: a -> a -> Ordering Source

(<) :: a -> a -> Bool infix 4 Source

(<=) :: a -> a -> Bool infix 4 Source

(>) :: a -> a -> Bool infix 4 Source

(>=) :: a -> a -> Bool infix 4 Source

max :: a -> a -> a Source

min :: a -> a -> a Source

Instances
Instances details
Ord ByteArray Source

Non-lexicographic ordering. This compares the lengths of the byte arrays first and uses a lexicographic ordering if the lengths are equal. Subject to change between major versions.

Since: base-4.17.0.0

Instance details

Defined in Data.Array.Byte

Ord BigNat
Instance details

Defined in GHC.Num.BigNat

Ord Void Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Base

Methods

compare :: Void -> Void -> Ordering Source

(<) :: Void -> Void -> Bool Source

(<=) :: Void -> Void -> Bool Source

(>) :: Void -> Void -> Bool Source

(>=) :: Void -> Void -> Bool Source

max :: Void -> Void -> Void Source

min :: Void -> Void -> Void Source

Ord ByteOrder Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.ByteOrder

Ord ClosureType Source
Instance details

Defined in GHC.Internal.ClosureTypes

Ord BlockReason Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Ord ThreadId Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Ord ThreadStatus Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Ord All Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering Source

(<) :: All -> All -> Bool Source

(<=) :: All -> All -> Bool Source

(>) :: All -> All -> Bool Source

(>=) :: All -> All -> Bool Source

max :: All -> All -> All Source

min :: All -> All -> All Source

Ord Any Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering Source

(<) :: Any -> Any -> Bool Source

(<=) :: Any -> Any -> Bool Source

(>) :: Any -> Any -> Bool Source

(>=) :: Any -> Any -> Bool Source

max :: Any -> Any -> Any Source

min :: Any -> Any -> Any Source

Ord SomeTypeRep Source
Instance details

Defined in GHC.Internal.Data.Typeable.Internal

Ord Unique Source
Instance details

Defined in GHC.Internal.Data.Unique

Ord Version Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Version

Ord TimeoutKey Source
Instance details

Defined in GHC.Internal.Event.TimeOut

Ord Unique Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Unique

Methods

compare :: Unique -> Unique -> Ordering Source

(<) :: Unique -> Unique -> Bool Source

(<=) :: Unique -> Unique -> Bool Source

(>) :: Unique -> Unique -> Bool Source

(>=) :: Unique -> Unique -> Bool Source

max :: Unique -> Unique -> Unique Source

min :: Unique -> Unique -> Unique Source

Ord ErrorCall Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Exception

Ord ArithException Source

Since: base-3.0

Instance details

Defined in GHC.Internal.Exception.Type

Ord Fingerprint Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Fingerprint.Type

Ord CBool Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CClock Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CDouble Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CFloat Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

compare :: CInt -> CInt -> Ordering Source

(<) :: CInt -> CInt -> Bool Source

(<=) :: CInt -> CInt -> Bool Source

(>) :: CInt -> CInt -> Bool Source

(>=) :: CInt -> CInt -> Bool Source

max :: CInt -> CInt -> CInt Source

min :: CInt -> CInt -> CInt Source

Ord CIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CLLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CPtrdiff Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CSChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CSUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CSigAtomic Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CSize Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CTime Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CUChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CUInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CUIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CUIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CULLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CULong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CUShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord CWchar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Ord IntPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Ord WordPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Ord Associativity Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

Ord DecidedStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Ord Fixity Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

Ord SourceStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Ord SourceUnpackedness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Ord SeekMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Device

Ord ArrayException Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Ord AsyncException Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Ord ExitCode Source
Instance details

Defined in GHC.Internal.IO.Exception

Ord BufferMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Ord Newline Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Ord NewlineMode Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Ord IOMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.IOMode

Ord Int16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Ord Int32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Ord Int64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Ord Int8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Methods

compare :: Int8 -> Int8 -> Ordering Source

(<) :: Int8 -> Int8 -> Bool Source

(<=) :: Int8 -> Int8 -> Bool Source

(>) :: Int8 -> Int8 -> Bool Source

(>=) :: Int8 -> Int8 -> Bool Source

max :: Int8 -> Int8 -> Int8 Source

min :: Int8 -> Int8 -> Int8 Source

Ord Extension Source
Instance details

Defined in GHC.Internal.LanguageExtensions

Ord CBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CBlkSize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CCc Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

compare :: CCc -> CCc -> Ordering Source

(<) :: CCc -> CCc -> Bool Source

(<=) :: CCc -> CCc -> Bool Source

(>) :: CCc -> CCc -> Bool Source

(>=) :: CCc -> CCc -> Bool Source

max :: CCc -> CCc -> CCc Source

min :: CCc -> CCc -> CCc Source

Ord CClockId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CDev Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

compare :: CDev -> CDev -> Ordering Source

(<) :: CDev -> CDev -> Bool Source

(<=) :: CDev -> CDev -> Bool Source

(>) :: CDev -> CDev -> Bool Source

(>=) :: CDev -> CDev -> Bool Source

max :: CDev -> CDev -> CDev Source

min :: CDev -> CDev -> CDev Source

Ord CFsBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CFsFilCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CGid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

compare :: CGid -> CGid -> Ordering Source

(<) :: CGid -> CGid -> Bool Source

(<=) :: CGid -> CGid -> Bool Source

(>) :: CGid -> CGid -> Bool Source

(>=) :: CGid -> CGid -> Bool Source

max :: CGid -> CGid -> CGid Source

min :: CGid -> CGid -> CGid Source

Ord CId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

compare :: CId -> CId -> Ordering Source

(<) :: CId -> CId -> Bool Source

(<=) :: CId -> CId -> Bool Source

(>) :: CId -> CId -> Bool Source

(>=) :: CId -> CId -> Bool Source

max :: CId -> CId -> CId Source

min :: CId -> CId -> CId Source

Ord CIno Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

compare :: CIno -> CIno -> Ordering Source

(<) :: CIno -> CIno -> Bool Source

(<=) :: CIno -> CIno -> Bool Source

(>) :: CIno -> CIno -> Bool Source

(>=) :: CIno -> CIno -> Bool Source

max :: CIno -> CIno -> CIno Source

min :: CIno -> CIno -> CIno Source

Ord CKey Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

compare :: CKey -> CKey -> Ordering Source

(<) :: CKey -> CKey -> Bool Source

(<=) :: CKey -> CKey -> Bool Source

(>) :: CKey -> CKey -> Bool Source

(>=) :: CKey -> CKey -> Bool Source

max :: CKey -> CKey -> CKey Source

min :: CKey -> CKey -> CKey Source

Ord CMode Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CNfds Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CNlink Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord COff Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

compare :: COff -> COff -> Ordering Source

(<) :: COff -> COff -> Bool Source

(<=) :: COff -> COff -> Bool Source

(>) :: COff -> COff -> Bool Source

(>=) :: COff -> COff -> Bool Source

max :: COff -> COff -> COff Source

min :: COff -> COff -> COff Source

Ord CPid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

compare :: CPid -> CPid -> Ordering Source

(<) :: CPid -> CPid -> Bool Source

(<=) :: CPid -> CPid -> Bool Source

(>) :: CPid -> CPid -> Bool Source

(>=) :: CPid -> CPid -> Bool Source

max :: CPid -> CPid -> CPid Source

min :: CPid -> CPid -> CPid Source

Ord CRLim Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CSocklen Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CSpeed Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CSsize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CTcflag Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CTimer Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Ord CUid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

compare :: CUid -> CUid -> Ordering Source

(<) :: CUid -> CUid -> Bool Source

(<=) :: CUid -> CUid -> Bool Source

(>) :: CUid -> CUid -> Bool Source

(>=) :: CUid -> CUid -> Bool Source

max :: CUid -> CUid -> CUid Source

min :: CUid -> CUid -> CUid Source

Ord Fd Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

compare :: Fd -> Fd -> Ordering Source

(<) :: Fd -> Fd -> Bool Source

(<=) :: Fd -> Fd -> Bool Source

(>) :: Fd -> Fd -> Bool Source

(>=) :: Fd -> Fd -> Bool Source

max :: Fd -> Fd -> Fd Source

min :: Fd -> Fd -> Fd Source

Ord AnnLookup Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord AnnTarget Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Bang Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Bang -> Bang -> Ordering Source

(<) :: Bang -> Bang -> Bool Source

(<=) :: Bang -> Bang -> Bool Source

(>) :: Bang -> Bang -> Bool Source

(>=) :: Bang -> Bang -> Bool Source

max :: Bang -> Bang -> Bang Source

min :: Bang -> Bang -> Bang Source

Ord BndrVis Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Body Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Body -> Body -> Ordering Source

(<) :: Body -> Body -> Bool Source

(<=) :: Body -> Body -> Bool Source

(>) :: Body -> Body -> Bool Source

(>=) :: Body -> Body -> Bool Source

max :: Body -> Body -> Body Source

min :: Body -> Body -> Body Source

Ord Bytes Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Callconv Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Clause Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Con Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Con -> Con -> Ordering Source

(<) :: Con -> Con -> Bool Source

(<=) :: Con -> Con -> Bool Source

(>) :: Con -> Con -> Bool Source

(>=) :: Con -> Con -> Bool Source

max :: Con -> Con -> Con Source

min :: Con -> Con -> Con Source

Ord Dec Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Dec -> Dec -> Ordering Source

(<) :: Dec -> Dec -> Bool Source

(<=) :: Dec -> Dec -> Bool Source

(>) :: Dec -> Dec -> Bool Source

(>=) :: Dec -> Dec -> Bool Source

max :: Dec -> Dec -> Dec Source

min :: Dec -> Dec -> Dec Source

Ord DecidedStrictness Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord DerivClause Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord DerivStrategy Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord DocLoc Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Exp Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Exp -> Exp -> Ordering Source

(<) :: Exp -> Exp -> Bool Source

(<=) :: Exp -> Exp -> Bool Source

(>) :: Exp -> Exp -> Bool Source

(>=) :: Exp -> Exp -> Bool Source

max :: Exp -> Exp -> Exp Source

min :: Exp -> Exp -> Exp Source

Ord FamilyResultSig Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Fixity Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord FixityDirection Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Foreign Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord FunDep Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Guard Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Info Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Info -> Info -> Ordering Source

(<) :: Info -> Info -> Bool Source

(<=) :: Info -> Info -> Bool Source

(>) :: Info -> Info -> Bool Source

(>=) :: Info -> Info -> Bool Source

max :: Info -> Info -> Info Source

min :: Info -> Info -> Info Source

Ord InjectivityAnn Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Inline Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Lit Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Lit -> Lit -> Ordering Source

(<) :: Lit -> Lit -> Bool Source

(<=) :: Lit -> Lit -> Bool Source

(>) :: Lit -> Lit -> Bool Source

(>=) :: Lit -> Lit -> Bool Source

max :: Lit -> Lit -> Lit Source

min :: Lit -> Lit -> Lit Source

Ord Loc Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Loc -> Loc -> Ordering Source

(<) :: Loc -> Loc -> Bool Source

(<=) :: Loc -> Loc -> Bool Source

(>) :: Loc -> Loc -> Bool Source

(>=) :: Loc -> Loc -> Bool Source

max :: Loc -> Loc -> Loc Source

min :: Loc -> Loc -> Loc Source

Ord Match Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord ModName Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Module Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord ModuleInfo Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Name Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Name -> Name -> Ordering Source

(<) :: Name -> Name -> Bool Source

(<=) :: Name -> Name -> Bool Source

(>) :: Name -> Name -> Bool Source

(>=) :: Name -> Name -> Bool Source

max :: Name -> Name -> Name Source

min :: Name -> Name -> Name Source

Ord NameFlavour Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord NameSpace Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord NamespaceSpecifier Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord OccName Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Overlap Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Pat Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Pat -> Pat -> Ordering Source

(<) :: Pat -> Pat -> Bool Source

(<=) :: Pat -> Pat -> Bool Source

(>) :: Pat -> Pat -> Bool Source

(>=) :: Pat -> Pat -> Bool Source

max :: Pat -> Pat -> Pat Source

min :: Pat -> Pat -> Pat Source

Ord PatSynArgs Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord PatSynDir Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Phases Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord PkgName Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Pragma Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Range Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Role Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Role -> Role -> Ordering Source

(<) :: Role -> Role -> Bool Source

(<=) :: Role -> Role -> Bool Source

(>) :: Role -> Role -> Bool Source

(>=) :: Role -> Role -> Bool Source

max :: Role -> Role -> Role Source

min :: Role -> Role -> Role Source

Ord RuleBndr Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord RuleMatch Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Safety Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord SourceStrictness Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord SourceUnpackedness Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Specificity Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Stmt Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Stmt -> Stmt -> Ordering Source

(<) :: Stmt -> Stmt -> Bool Source

(<=) :: Stmt -> Stmt -> Bool Source

(>) :: Stmt -> Stmt -> Bool Source

(>=) :: Stmt -> Stmt -> Bool Source

max :: Stmt -> Stmt -> Stmt Source

min :: Stmt -> Stmt -> Stmt Source

Ord TyLit Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord TySynEqn Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord Type Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: Type -> Type -> Ordering Source

(<) :: Type -> Type -> Bool Source

(<=) :: Type -> Type -> Bool Source

(>) :: Type -> Type -> Bool Source

(>=) :: Type -> Type -> Bool Source

max :: Type -> Type -> Type Source

min :: Type -> Type -> Type Source

Ord TypeFamilyHead Source
Instance details

Defined in GHC.Internal.TH.Syntax

Ord SomeChar Source
Instance details

Defined in GHC.Internal.TypeLits

Ord SomeSymbol Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.TypeLits

Ord SomeNat Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.TypeNats

Ord GeneralCategory Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Unicode

Ord Word16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Ord Word32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Ord Word64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Ord Word8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Ord Ordering Source
Instance details

Defined in GHC.Classes

Ord TyCon Source
Instance details

Defined in GHC.Classes

Ord Integer
Instance details

Defined in GHC.Num.Integer

Ord Natural
Instance details

Defined in GHC.Num.Natural

Ord () Source
Instance details

Defined in GHC.Classes

Methods

compare :: () -> () -> Ordering Source

(<) :: () -> () -> Bool Source

(<=) :: () -> () -> Bool Source

(>) :: () -> () -> Bool Source

(>=) :: () -> () -> Bool Source

max :: () -> () -> () Source

min :: () -> () -> () Source

Ord Bool Source
Instance details

Defined in GHC.Classes

Methods

compare :: Bool -> Bool -> Ordering Source

(<) :: Bool -> Bool -> Bool Source

(<=) :: Bool -> Bool -> Bool Source

(>) :: Bool -> Bool -> Bool Source

(>=) :: Bool -> Bool -> Bool Source

max :: Bool -> Bool -> Bool Source

min :: Bool -> Bool -> Bool Source

Ord Char Source
Instance details

Defined in GHC.Classes

Methods

compare :: Char -> Char -> Ordering Source

(<) :: Char -> Char -> Bool Source

(<=) :: Char -> Char -> Bool Source

(>) :: Char -> Char -> Bool Source

(>=) :: Char -> Char -> Bool Source

max :: Char -> Char -> Char Source

min :: Char -> Char -> Char Source

Ord Double Source

IEEE 754 Double-precision type includes not only numbers, but also positive and negative infinities and a special element called NaN (which can be quiet or signal).

IEEE 754-2008, section 5.11 requires that if at least one of arguments of <=, <, >, >= is NaN then the result of the comparison is False, and instance Ord Double complies with this requirement. This violates the reflexivity: both NaN <= NaN and NaN >= NaN are False.

IEEE 754-2008, section 5.10 defines totalOrder predicate. Unfortunately, compare on Doubles violates the IEEE standard and does not define a total order. More specifically, both compare NaN x and compare x NaN always return GT.

Thus, users must be extremely cautious when using instance Ord Double. For instance, one should avoid ordered containers with keys represented by Double, because data loss and corruption may happen. An IEEE-compliant compare is available in fp-ieee package as TotallyOrdered newtype.

Moving further, the behaviour of min and max with regards to NaN is also non-compliant. IEEE 754-2008, section 5.3.1 defines that quiet NaN should be treated as a missing data by minNum and maxNum functions, for example, minNum(NaN, 1) = minNum(1, NaN) = 1. Some languages such as Java deviate from the standard implementing minNum(NaN, 1) = minNum(1, NaN) = NaN. However, min / max in base are even worse: min NaN 1 is 1, but min 1 NaN is NaN.

IEEE 754-2008 compliant min / max can be found in ieee754 package under minNum / maxNum names. Implementations compliant with minimumNumber / maximumNumber from a newer IEEE 754-2019, section 9.6 are available from fp-ieee package.

Instance details

Defined in GHC.Classes

Ord Float Source

See instance Ord Double for discussion of deviations from IEEE 754 standard.

Instance details

Defined in GHC.Classes

Ord Int Source
Instance details

Defined in GHC.Classes

Methods

compare :: Int -> Int -> Ordering Source

(<) :: Int -> Int -> Bool Source

(<=) :: Int -> Int -> Bool Source

(>) :: Int -> Int -> Bool Source

(>=) :: Int -> Int -> Bool Source

max :: Int -> Int -> Int Source

min :: Int -> Int -> Int Source

Ord Word Source
Instance details

Defined in GHC.Classes

Methods

compare :: Word -> Word -> Ordering Source

(<) :: Word -> Word -> Bool Source

(<=) :: Word -> Word -> Bool Source

(>) :: Word -> Word -> Bool Source

(>=) :: Word -> Word -> Bool Source

max :: Word -> Word -> Word Source

min :: Word -> Word -> Word Source

Ord a => Ord (First a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: First a -> First a -> Ordering Source

(<) :: First a -> First a -> Bool Source

(<=) :: First a -> First a -> Bool Source

(>) :: First a -> First a -> Bool Source

(>=) :: First a -> First a -> Bool Source

max :: First a -> First a -> First a Source

min :: First a -> First a -> First a Source

Ord a => Ord (Last a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Last a -> Last a -> Ordering Source

(<) :: Last a -> Last a -> Bool Source

(<=) :: Last a -> Last a -> Bool Source

(>) :: Last a -> Last a -> Bool Source

(>=) :: Last a -> Last a -> Bool Source

max :: Last a -> Last a -> Last a Source

min :: Last a -> Last a -> Last a Source

Ord a => Ord (Max a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Max a -> Max a -> Ordering Source

(<) :: Max a -> Max a -> Bool Source

(<=) :: Max a -> Max a -> Bool Source

(>) :: Max a -> Max a -> Bool Source

(>=) :: Max a -> Max a -> Bool Source

max :: Max a -> Max a -> Max a Source

min :: Max a -> Max a -> Max a Source

Ord a => Ord (Min a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Min a -> Min a -> Ordering Source

(<) :: Min a -> Min a -> Bool Source

(<=) :: Min a -> Min a -> Bool Source

(>) :: Min a -> Min a -> Bool Source

(>=) :: Min a -> Min a -> Bool Source

max :: Min a -> Min a -> Min a Source

min :: Min a -> Min a -> Min a Source

Ord m => Ord (WrappedMonoid m) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Ord a => Ord (NonEmpty a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Ord a => Ord (Identity a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Ord a => Ord (First a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

compare :: First a -> First a -> Ordering Source

(<) :: First a -> First a -> Bool Source

(<=) :: First a -> First a -> Bool Source

(>) :: First a -> First a -> Bool Source

(>=) :: First a -> First a -> Bool Source

max :: First a -> First a -> First a Source

min :: First a -> First a -> First a Source

Ord a => Ord (Last a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

compare :: Last a -> Last a -> Ordering Source

(<) :: Last a -> Last a -> Bool Source

(<=) :: Last a -> Last a -> Bool Source

(>) :: Last a -> Last a -> Bool Source

(>=) :: Last a -> Last a -> Bool Source

max :: Last a -> Last a -> Last a Source

min :: Last a -> Last a -> Last a Source

Ord a => Ord (Down a) Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

compare :: Down a -> Down a -> Ordering Source

(<) :: Down a -> Down a -> Bool Source

(<=) :: Down a -> Down a -> Bool Source

(>) :: Down a -> Down a -> Bool Source

(>=) :: Down a -> Down a -> Bool Source

max :: Down a -> Down a -> Down a Source

min :: Down a -> Down a -> Down a Source

Ord a => Ord (Dual a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Dual a -> Dual a -> Ordering Source

(<) :: Dual a -> Dual a -> Bool Source

(<=) :: Dual a -> Dual a -> Bool Source

(>) :: Dual a -> Dual a -> Bool Source

(>=) :: Dual a -> Dual a -> Bool Source

max :: Dual a -> Dual a -> Dual a Source

min :: Dual a -> Dual a -> Dual a Source

Ord a => Ord (Product a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Product a -> Product a -> Ordering Source

(<) :: Product a -> Product a -> Bool Source

(<=) :: Product a -> Product a -> Bool Source

(>) :: Product a -> Product a -> Bool Source

(>=) :: Product a -> Product a -> Bool Source

max :: Product a -> Product a -> Product a Source

min :: Product a -> Product a -> Product a Source

Ord a => Ord (Sum a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Sum a -> Sum a -> Ordering Source

(<) :: Sum a -> Sum a -> Bool Source

(<=) :: Sum a -> Sum a -> Bool Source

(>) :: Sum a -> Sum a -> Bool Source

(>=) :: Sum a -> Sum a -> Bool Source

max :: Sum a -> Sum a -> Sum a Source

min :: Sum a -> Sum a -> Sum a Source

Ord (ConstPtr a) Source
Instance details

Defined in GHC.Internal.Foreign.C.ConstPtr

Ord (ForeignPtr a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.ForeignPtr

Ord a => Ord (ZipList a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

compare :: ZipList a -> ZipList a -> Ordering Source

(<) :: ZipList a -> ZipList a -> Bool Source

(<=) :: ZipList a -> ZipList a -> Bool Source

(>) :: ZipList a -> ZipList a -> Bool Source

(>=) :: ZipList a -> ZipList a -> Bool Source

max :: ZipList a -> ZipList a -> ZipList a Source

min :: ZipList a -> ZipList a -> ZipList a Source

Ord p => Ord (Par1 p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: Par1 p -> Par1 p -> Ordering Source

(<) :: Par1 p -> Par1 p -> Bool Source

(<=) :: Par1 p -> Par1 p -> Bool Source

(>) :: Par1 p -> Par1 p -> Bool Source

(>=) :: Par1 p -> Par1 p -> Bool Source

max :: Par1 p -> Par1 p -> Par1 p Source

min :: Par1 p -> Par1 p -> Par1 p Source

Ord (FunPtr a) Source
Instance details

Defined in GHC.Internal.Ptr

Methods

compare :: FunPtr a -> FunPtr a -> Ordering Source

(<) :: FunPtr a -> FunPtr a -> Bool Source

(<=) :: FunPtr a -> FunPtr a -> Bool Source

(>) :: FunPtr a -> FunPtr a -> Bool Source

(>=) :: FunPtr a -> FunPtr a -> Bool Source

max :: FunPtr a -> FunPtr a -> FunPtr a Source

min :: FunPtr a -> FunPtr a -> FunPtr a Source

Ord (Ptr a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Ptr

Methods

compare :: Ptr a -> Ptr a -> Ordering Source

(<) :: Ptr a -> Ptr a -> Bool Source

(<=) :: Ptr a -> Ptr a -> Bool Source

(>) :: Ptr a -> Ptr a -> Bool Source

(>=) :: Ptr a -> Ptr a -> Bool Source

max :: Ptr a -> Ptr a -> Ptr a Source

min :: Ptr a -> Ptr a -> Ptr a Source

Integral a => Ord (Ratio a) Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Methods

compare :: Ratio a -> Ratio a -> Ordering Source

(<) :: Ratio a -> Ratio a -> Bool Source

(<=) :: Ratio a -> Ratio a -> Bool Source

(>) :: Ratio a -> Ratio a -> Bool Source

(>=) :: Ratio a -> Ratio a -> Bool Source

max :: Ratio a -> Ratio a -> Ratio a Source

min :: Ratio a -> Ratio a -> Ratio a Source

Ord flag => Ord (TyVarBndr flag) Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

compare :: TyVarBndr flag -> TyVarBndr flag -> Ordering Source

(<) :: TyVarBndr flag -> TyVarBndr flag -> Bool Source

(<=) :: TyVarBndr flag -> TyVarBndr flag -> Bool Source

(>) :: TyVarBndr flag -> TyVarBndr flag -> Bool Source

(>=) :: TyVarBndr flag -> TyVarBndr flag -> Bool Source

max :: TyVarBndr flag -> TyVarBndr flag -> TyVarBndr flag Source

min :: TyVarBndr flag -> TyVarBndr flag -> TyVarBndr flag Source

Ord (SChar c) Source

Since: base-4.19.0.0

Instance details

Defined in GHC.Internal.TypeLits

Methods

compare :: SChar c -> SChar c -> Ordering Source

(<) :: SChar c -> SChar c -> Bool Source

(<=) :: SChar c -> SChar c -> Bool Source

(>) :: SChar c -> SChar c -> Bool Source

(>=) :: SChar c -> SChar c -> Bool Source

max :: SChar c -> SChar c -> SChar c Source

min :: SChar c -> SChar c -> SChar c Source

Ord (SSymbol s) Source

Since: base-4.19.0.0

Instance details

Defined in GHC.Internal.TypeLits

Methods

compare :: SSymbol s -> SSymbol s -> Ordering Source

(<) :: SSymbol s -> SSymbol s -> Bool Source

(<=) :: SSymbol s -> SSymbol s -> Bool Source

(>) :: SSymbol s -> SSymbol s -> Bool Source

(>=) :: SSymbol s -> SSymbol s -> Bool Source

max :: SSymbol s -> SSymbol s -> SSymbol s Source

min :: SSymbol s -> SSymbol s -> SSymbol s Source

Ord (SNat n) Source

Since: base-4.19.0.0

Instance details

Defined in GHC.Internal.TypeNats

Methods

compare :: SNat n -> SNat n -> Ordering Source

(<) :: SNat n -> SNat n -> Bool Source

(<=) :: SNat n -> SNat n -> Bool Source

(>) :: SNat n -> SNat n -> Bool Source

(>=) :: SNat n -> SNat n -> Bool Source

max :: SNat n -> SNat n -> SNat n Source

min :: SNat n -> SNat n -> SNat n Source

Ord a => Ord (Maybe a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Maybe

Methods

compare :: Maybe a -> Maybe a -> Ordering Source

(<) :: Maybe a -> Maybe a -> Bool Source

(<=) :: Maybe a -> Maybe a -> Bool Source

(>) :: Maybe a -> Maybe a -> Bool Source

(>=) :: Maybe a -> Maybe a -> Bool Source

max :: Maybe a -> Maybe a -> Maybe a Source

min :: Maybe a -> Maybe a -> Maybe a Source

Ord a => Ord (Solo a) Source
Instance details

Defined in GHC.Classes

Methods

compare :: Solo a -> Solo a -> Ordering Source

(<) :: Solo a -> Solo a -> Bool Source

(<=) :: Solo a -> Solo a -> Bool Source

(>) :: Solo a -> Solo a -> Bool Source

(>=) :: Solo a -> Solo a -> Bool Source

max :: Solo a -> Solo a -> Solo a Source

min :: Solo a -> Solo a -> Solo a Source

Ord a => Ord [a] Source
Instance details

Defined in GHC.Classes

Methods

compare :: [a] -> [a] -> Ordering Source

(<) :: [a] -> [a] -> Bool Source

(<=) :: [a] -> [a] -> Bool Source

(>) :: [a] -> [a] -> Bool Source

(>=) :: [a] -> [a] -> Bool Source

max :: [a] -> [a] -> [a] Source

min :: [a] -> [a] -> [a] Source

Ord (Fixed a) Source

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

compare :: Fixed a -> Fixed a -> Ordering Source

(<) :: Fixed a -> Fixed a -> Bool Source

(<=) :: Fixed a -> Fixed a -> Bool Source

(>) :: Fixed a -> Fixed a -> Bool Source

(>=) :: Fixed a -> Fixed a -> Bool Source

max :: Fixed a -> Fixed a -> Fixed a Source

min :: Fixed a -> Fixed a -> Fixed a Source

Ord a => Ord (Arg a b) Source

Note that Arg's Ord instance has min and max implementations that differ from the tie-breaking conventions of the default implementation of min and max in class Ord; Arg breaks ties by favoring the first argument in both functions.

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Arg a b -> Arg a b -> Ordering Source

(<) :: Arg a b -> Arg a b -> Bool Source

(<=) :: Arg a b -> Arg a b -> Bool Source

(>) :: Arg a b -> Arg a b -> Bool Source

(>=) :: Arg a b -> Arg a b -> Bool Source

max :: Arg a b -> Arg a b -> Arg a b Source

min :: Arg a b -> Arg a b -> Arg a b Source

(Ix i, Ord e) => Ord (Array i e) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Arr

Methods

compare :: Array i e -> Array i e -> Ordering Source

(<) :: Array i e -> Array i e -> Bool Source

(<=) :: Array i e -> Array i e -> Bool Source

(>) :: Array i e -> Array i e -> Bool Source

(>=) :: Array i e -> Array i e -> Bool Source

max :: Array i e -> Array i e -> Array i e Source

min :: Array i e -> Array i e -> Array i e Source

(Ord a, Ord b) => Ord (Either a b) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Either

Methods

compare :: Either a b -> Either a b -> Ordering Source

(<) :: Either a b -> Either a b -> Bool Source

(<=) :: Either a b -> Either a b -> Bool Source

(>) :: Either a b -> Either a b -> Bool Source

(>=) :: Either a b -> Either a b -> Bool Source

max :: Either a b -> Either a b -> Either a b Source

min :: Either a b -> Either a b -> Either a b Source

Ord (Proxy s) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

compare :: Proxy s -> Proxy s -> Ordering Source

(<) :: Proxy s -> Proxy s -> Bool Source

(<=) :: Proxy s -> Proxy s -> Bool Source

(>) :: Proxy s -> Proxy s -> Bool Source

(>=) :: Proxy s -> Proxy s -> Bool Source

max :: Proxy s -> Proxy s -> Proxy s Source

min :: Proxy s -> Proxy s -> Proxy s Source

Ord (TypeRep a) Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Data.Typeable.Internal

Methods

compare :: TypeRep a -> TypeRep a -> Ordering Source

(<) :: TypeRep a -> TypeRep a -> Bool Source

(<=) :: TypeRep a -> TypeRep a -> Bool Source

(>) :: TypeRep a -> TypeRep a -> Bool Source

(>=) :: TypeRep a -> TypeRep a -> Bool Source

max :: TypeRep a -> TypeRep a -> TypeRep a Source

min :: TypeRep a -> TypeRep a -> TypeRep a Source

Ord (U1 p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: U1 p -> U1 p -> Ordering Source

(<) :: U1 p -> U1 p -> Bool Source

(<=) :: U1 p -> U1 p -> Bool Source

(>) :: U1 p -> U1 p -> Bool Source

(>=) :: U1 p -> U1 p -> Bool Source

max :: U1 p -> U1 p -> U1 p Source

min :: U1 p -> U1 p -> U1 p Source

Ord (V1 p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: V1 p -> V1 p -> Ordering Source

(<) :: V1 p -> V1 p -> Bool Source

(<=) :: V1 p -> V1 p -> Bool Source

(>) :: V1 p -> V1 p -> Bool Source

(>=) :: V1 p -> V1 p -> Bool Source

max :: V1 p -> V1 p -> V1 p Source

min :: V1 p -> V1 p -> V1 p Source

(Ord a, Ord b) => Ord (a, b) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b) -> (a, b) -> Ordering Source

(<) :: (a, b) -> (a, b) -> Bool Source

(<=) :: (a, b) -> (a, b) -> Bool Source

(>) :: (a, b) -> (a, b) -> Bool Source

(>=) :: (a, b) -> (a, b) -> Bool Source

max :: (a, b) -> (a, b) -> (a, b) Source

min :: (a, b) -> (a, b) -> (a, b) Source

Ord a => Ord (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

compare :: Const a b -> Const a b -> Ordering Source

(<) :: Const a b -> Const a b -> Bool Source

(<=) :: Const a b -> Const a b -> Bool Source

(>) :: Const a b -> Const a b -> Bool Source

(>=) :: Const a b -> Const a b -> Bool Source

max :: Const a b -> Const a b -> Const a b Source

min :: Const a b -> Const a b -> Const a b Source

Ord (f a) => Ord (Ap f a) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

compare :: Ap f a -> Ap f a -> Ordering Source

(<) :: Ap f a -> Ap f a -> Bool Source

(<=) :: Ap f a -> Ap f a -> Bool Source

(>) :: Ap f a -> Ap f a -> Bool Source

(>=) :: Ap f a -> Ap f a -> Bool Source

max :: Ap f a -> Ap f a -> Ap f a Source

min :: Ap f a -> Ap f a -> Ap f a Source

Ord (f a) => Ord (Alt f a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Alt f a -> Alt f a -> Ordering Source

(<) :: Alt f a -> Alt f a -> Bool Source

(<=) :: Alt f a -> Alt f a -> Bool Source

(>) :: Alt f a -> Alt f a -> Bool Source

(>=) :: Alt f a -> Alt f a -> Bool Source

max :: Alt f a -> Alt f a -> Alt f a Source

min :: Alt f a -> Alt f a -> Alt f a Source

Ord (Coercion a b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Coercion

Methods

compare :: Coercion a b -> Coercion a b -> Ordering Source

(<) :: Coercion a b -> Coercion a b -> Bool Source

(<=) :: Coercion a b -> Coercion a b -> Bool Source

(>) :: Coercion a b -> Coercion a b -> Bool Source

(>=) :: Coercion a b -> Coercion a b -> Bool Source

max :: Coercion a b -> Coercion a b -> Coercion a b Source

min :: Coercion a b -> Coercion a b -> Coercion a b Source

Ord (a :~: b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

Methods

compare :: (a :~: b) -> (a :~: b) -> Ordering Source

(<) :: (a :~: b) -> (a :~: b) -> Bool Source

(<=) :: (a :~: b) -> (a :~: b) -> Bool Source

(>) :: (a :~: b) -> (a :~: b) -> Bool Source

(>=) :: (a :~: b) -> (a :~: b) -> Bool Source

max :: (a :~: b) -> (a :~: b) -> a :~: b Source

min :: (a :~: b) -> (a :~: b) -> a :~: b Source

(Generic1 f, Ord (Rep1 f a)) => Ord (Generically1 f a) Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.Generics

Ord (f p) => Ord (Rec1 f p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: Rec1 f p -> Rec1 f p -> Ordering Source

(<) :: Rec1 f p -> Rec1 f p -> Bool Source

(<=) :: Rec1 f p -> Rec1 f p -> Bool Source

(>) :: Rec1 f p -> Rec1 f p -> Bool Source

(>=) :: Rec1 f p -> Rec1 f p -> Bool Source

max :: Rec1 f p -> Rec1 f p -> Rec1 f p Source

min :: Rec1 f p -> Rec1 f p -> Rec1 f p Source

Ord (URec (Ptr ()) p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering Source

(<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source

(<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source

(>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source

(>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source

max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p Source

min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p Source

Ord (URec Char p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: URec Char p -> URec Char p -> Ordering Source

(<) :: URec Char p -> URec Char p -> Bool Source

(<=) :: URec Char p -> URec Char p -> Bool Source

(>) :: URec Char p -> URec Char p -> Bool Source

(>=) :: URec Char p -> URec Char p -> Bool Source

max :: URec Char p -> URec Char p -> URec Char p Source

min :: URec Char p -> URec Char p -> URec Char p Source

Ord (URec Double p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Ord (URec Float p) Source
Instance details

Defined in GHC.Internal.Generics

Ord (URec Int p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: URec Int p -> URec Int p -> Ordering Source

(<) :: URec Int p -> URec Int p -> Bool Source

(<=) :: URec Int p -> URec Int p -> Bool Source

(>) :: URec Int p -> URec Int p -> Bool Source

(>=) :: URec Int p -> URec Int p -> Bool Source

max :: URec Int p -> URec Int p -> URec Int p Source

min :: URec Int p -> URec Int p -> URec Int p Source

Ord (URec Word p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: URec Word p -> URec Word p -> Ordering Source

(<) :: URec Word p -> URec Word p -> Bool Source

(<=) :: URec Word p -> URec Word p -> Bool Source

(>) :: URec Word p -> URec Word p -> Bool Source

(>=) :: URec Word p -> URec Word p -> Bool Source

max :: URec Word p -> URec Word p -> URec Word p Source

min :: URec Word p -> URec Word p -> URec Word p Source

(Ord a, Ord b, Ord c) => Ord (a, b, c) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c) -> (a, b, c) -> Ordering Source

(<) :: (a, b, c) -> (a, b, c) -> Bool Source

(<=) :: (a, b, c) -> (a, b, c) -> Bool Source

(>) :: (a, b, c) -> (a, b, c) -> Bool Source

(>=) :: (a, b, c) -> (a, b, c) -> Bool Source

max :: (a, b, c) -> (a, b, c) -> (a, b, c) Source

min :: (a, b, c) -> (a, b, c) -> (a, b, c) Source

(Ord (f a), Ord (g a)) => Ord (Product f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Product

Methods

compare :: Product f g a -> Product f g a -> Ordering Source

(<) :: Product f g a -> Product f g a -> Bool Source

(<=) :: Product f g a -> Product f g a -> Bool Source

(>) :: Product f g a -> Product f g a -> Bool Source

(>=) :: Product f g a -> Product f g a -> Bool Source

max :: Product f g a -> Product f g a -> Product f g a Source

min :: Product f g a -> Product f g a -> Product f g a Source

(Ord (f a), Ord (g a)) => Ord (Sum f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Sum

Methods

compare :: Sum f g a -> Sum f g a -> Ordering Source

(<) :: Sum f g a -> Sum f g a -> Bool Source

(<=) :: Sum f g a -> Sum f g a -> Bool Source

(>) :: Sum f g a -> Sum f g a -> Bool Source

(>=) :: Sum f g a -> Sum f g a -> Bool Source

max :: Sum f g a -> Sum f g a -> Sum f g a Source

min :: Sum f g a -> Sum f g a -> Sum f g a Source

Ord (a :~~: b) Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

Methods

compare :: (a :~~: b) -> (a :~~: b) -> Ordering Source

(<) :: (a :~~: b) -> (a :~~: b) -> Bool Source

(<=) :: (a :~~: b) -> (a :~~: b) -> Bool Source

(>) :: (a :~~: b) -> (a :~~: b) -> Bool Source

(>=) :: (a :~~: b) -> (a :~~: b) -> Bool Source

max :: (a :~~: b) -> (a :~~: b) -> a :~~: b Source

min :: (a :~~: b) -> (a :~~: b) -> a :~~: b Source

(Ord (f p), Ord (g p)) => Ord ((f :*: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: (f :*: g) p -> (f :*: g) p -> Ordering Source

(<) :: (f :*: g) p -> (f :*: g) p -> Bool Source

(<=) :: (f :*: g) p -> (f :*: g) p -> Bool Source

(>) :: (f :*: g) p -> (f :*: g) p -> Bool Source

(>=) :: (f :*: g) p -> (f :*: g) p -> Bool Source

max :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source

min :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source

(Ord (f p), Ord (g p)) => Ord ((f :+: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: (f :+: g) p -> (f :+: g) p -> Ordering Source

(<) :: (f :+: g) p -> (f :+: g) p -> Bool Source

(<=) :: (f :+: g) p -> (f :+: g) p -> Bool Source

(>) :: (f :+: g) p -> (f :+: g) p -> Bool Source

(>=) :: (f :+: g) p -> (f :+: g) p -> Bool Source

max :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p Source

min :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p Source

Ord c => Ord (K1 i c p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: K1 i c p -> K1 i c p -> Ordering Source

(<) :: K1 i c p -> K1 i c p -> Bool Source

(<=) :: K1 i c p -> K1 i c p -> Bool Source

(>) :: K1 i c p -> K1 i c p -> Bool Source

(>=) :: K1 i c p -> K1 i c p -> Bool Source

max :: K1 i c p -> K1 i c p -> K1 i c p Source

min :: K1 i c p -> K1 i c p -> K1 i c p Source

(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d) -> (a, b, c, d) -> Ordering Source

(<) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source

(<=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source

(>) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source

(>=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source

max :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source

min :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source

Ord (f (g a)) => Ord (Compose f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Compose

Methods

compare :: Compose f g a -> Compose f g a -> Ordering Source

(<) :: Compose f g a -> Compose f g a -> Bool Source

(<=) :: Compose f g a -> Compose f g a -> Bool Source

(>) :: Compose f g a -> Compose f g a -> Bool Source

(>=) :: Compose f g a -> Compose f g a -> Bool Source

max :: Compose f g a -> Compose f g a -> Compose f g a Source

min :: Compose f g a -> Compose f g a -> Compose f g a Source

Ord (f (g p)) => Ord ((f :.: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: (f :.: g) p -> (f :.: g) p -> Ordering Source

(<) :: (f :.: g) p -> (f :.: g) p -> Bool Source

(<=) :: (f :.: g) p -> (f :.: g) p -> Bool Source

(>) :: (f :.: g) p -> (f :.: g) p -> Bool Source

(>=) :: (f :.: g) p -> (f :.: g) p -> Bool Source

max :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source

min :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source

Ord (f p) => Ord (M1 i c f p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: M1 i c f p -> M1 i c f p -> Ordering Source

(<) :: M1 i c f p -> M1 i c f p -> Bool Source

(<=) :: M1 i c f p -> M1 i c f p -> Bool Source

(>) :: M1 i c f p -> M1 i c f p -> Bool Source

(>=) :: M1 i c f p -> M1 i c f p -> Bool Source

max :: M1 i c f p -> M1 i c f p -> M1 i c f p Source

min :: M1 i c f p -> M1 i c f p -> M1 i c f p Source

(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering Source

(<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source

(<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source

(>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source

(>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source

max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source

min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering Source

(<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source

(<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source

(>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source

(>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source

max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source

min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering Source

(<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source

(<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source

(>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source

(>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source

max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source

min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering Source

(<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source

(<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source

(>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source

(>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source

max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) Source

min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) Source

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering Source

(<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source

(<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source

(>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source

(>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source

max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) Source

min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) Source

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering Source

(<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source

(<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source

(>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source

(>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source

max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) Source

min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) Source

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering Source

(<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source

(<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source

(>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source

(>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source

max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) Source

min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) Source

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering Source

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source

max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) Source

min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) Source

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering Source

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source

max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) Source

min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) Source

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering Source

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source

max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source

min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering Source

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source

max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source

min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source

class Enum a where Source

Class Enum defines operations on sequentially ordered types.

The enumFrom... methods are used in Haskell's translation of arithmetic sequences.

Instances of Enum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details.

For any type that is an instance of class Bounded as well as Enum, the following should hold:

   enumFrom     x   = enumFromTo     x maxBound
   enumFromThen x y = enumFromThenTo x y bound
     where
       bound | fromEnum y >= fromEnum x = maxBound
             | otherwise                = minBound

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a Source

Successor of a value. For numeric types, succ adds 1.

pred :: a -> a Source

Predecessor of a value. For numeric types, pred subtracts 1.

toEnum :: Int -> a Source

Convert from an Int.

fromEnum :: a -> Int Source

Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int.

enumFrom :: a -> [a] Source

Used in Haskell's translation of [n..] with [n..] = enumFrom n, a possible implementation being enumFrom n = n : enumFrom (succ n).

Examples
Expand
  • enumFrom 4 :: [Integer] = [4,5,6,7,...]
  • enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]

enumFromThen :: a -> a -> [a] Source

Used in Haskell's translation of [n,n'..] with [n,n'..] = enumFromThen n n', a possible implementation being enumFromThen n n' = n : n' : worker (f x) (f x n'), worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and

  f n y
    | n > 0 = f (n - 1) (succ y)
    | n < 0 = f (n + 1) (pred y)
    | otherwise = y
  
Examples
Expand
  • enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
  • enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]

enumFromTo :: a -> a -> [a] Source

Used in Haskell's translation of [n..m] with [n..m] = enumFromTo n m, a possible implementation being

  enumFromTo n m
     | n <= m = n : enumFromTo (succ n) m
     | otherwise = []
  
Examples
Expand
  • enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
  • enumFromTo 42 1 :: [Integer] = []

enumFromThenTo :: a -> a -> a -> [a] Source

Used in Haskell's translation of [n,n'..m] with [n,n'..m] = enumFromThenTo n n' m, a possible implementation being enumFromThenTo n n' m = worker (f x) (c x) n m, x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0)

  f n y
     | n > 0 = f (n - 1) (succ y)
     | n < 0 = f (n + 1) (pred y)
     | otherwise = y
  

and

  worker s c v m
     | c v m = v : worker s c (s v) m
     | otherwise = []
  
Examples
Expand
  • enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
  • enumFromThenTo 6 8 2 :: [Int] = []
Instances
Instances details
Enum ByteOrder Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.ByteOrder

Enum ClosureType Source
Instance details

Defined in GHC.Internal.ClosureTypes

Enum CBool Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CClock Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CDouble Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CFloat Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CLLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CPtrdiff Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CSChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CSUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CSigAtomic Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CSize Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CTime Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CUChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CUInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CUIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CUIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CULLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CULong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CUShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum CWchar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Enum IntPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Enum WordPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Enum Associativity Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Enum DecidedStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Enum SourceStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Enum SourceUnpackedness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Enum SeekMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Device

Enum IOMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.IOMode

Enum IoSubSystem Source
Instance details

Defined in GHC.Internal.IO.SubSystem

Enum Int16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Enum Int32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Enum Int64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Enum Int8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Enum Extension Source
Instance details

Defined in GHC.Internal.LanguageExtensions

Enum DoCostCentres Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Enum DoHeapProfile Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Enum DoTrace Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Enum GiveGCStats Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Enum IoManagerFlag Source
Instance details

Defined in GHC.Internal.RTS.Flags

Enum CBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CBlkSize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CCc Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CClockId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CDev Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CFsBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CFsFilCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CGid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CIno Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CKey Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CMode Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CNfds Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CNlink Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum COff Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CPid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CRLim Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CSocklen Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CSpeed Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CSsize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CTcflag Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum CUid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Enum Fd Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

succ :: Fd -> Fd Source

pred :: Fd -> Fd Source

toEnum :: Int -> Fd Source

fromEnum :: Fd -> Int Source

enumFrom :: Fd -> [Fd] Source

enumFromThen :: Fd -> Fd -> [Fd] Source

enumFromTo :: Fd -> Fd -> [Fd] Source

enumFromThenTo :: Fd -> Fd -> Fd -> [Fd] Source

Enum GeneralCategory Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Unicode

Enum Word16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Enum Word32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Enum Word64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Enum Word8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Enum Ordering Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Enum Integer Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Enum Natural Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Enum

Enum () Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

succ :: () -> () Source

pred :: () -> () Source

toEnum :: Int -> () Source

fromEnum :: () -> Int Source

enumFrom :: () -> [()] Source

enumFromThen :: () -> () -> [()] Source

enumFromTo :: () -> () -> [()] Source

enumFromThenTo :: () -> () -> () -> [()] Source

Enum Bool Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Enum Char Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Enum Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Enum Levity Source

Since: base-4.16.0.0

Instance details

Defined in GHC.Internal.Enum

Enum VecCount Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Enum

Enum VecElem Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Enum

Enum Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Enum a => Enum (First a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: First a -> First a Source

pred :: First a -> First a Source

toEnum :: Int -> First a Source

fromEnum :: First a -> Int Source

enumFrom :: First a -> [First a] Source

enumFromThen :: First a -> First a -> [First a] Source

enumFromTo :: First a -> First a -> [First a] Source

enumFromThenTo :: First a -> First a -> First a -> [First a] Source

Enum a => Enum (Last a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: Last a -> Last a Source

pred :: Last a -> Last a Source

toEnum :: Int -> Last a Source

fromEnum :: Last a -> Int Source

enumFrom :: Last a -> [Last a] Source

enumFromThen :: Last a -> Last a -> [Last a] Source

enumFromTo :: Last a -> Last a -> [Last a] Source

enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] Source

Enum a => Enum (Max a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: Max a -> Max a Source

pred :: Max a -> Max a Source

toEnum :: Int -> Max a Source

fromEnum :: Max a -> Int Source

enumFrom :: Max a -> [Max a] Source

enumFromThen :: Max a -> Max a -> [Max a] Source

enumFromTo :: Max a -> Max a -> [Max a] Source

enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] Source

Enum a => Enum (Min a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: Min a -> Min a Source

pred :: Min a -> Min a Source

toEnum :: Int -> Min a Source

fromEnum :: Min a -> Int Source

enumFrom :: Min a -> [Min a] Source

enumFromThen :: Min a -> Min a -> [Min a] Source

enumFromTo :: Min a -> Min a -> [Min a] Source

enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] Source

Enum a => Enum (WrappedMonoid a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Enum a => Enum (And a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

succ :: And a -> And a Source

pred :: And a -> And a Source

toEnum :: Int -> And a Source

fromEnum :: And a -> Int Source

enumFrom :: And a -> [And a] Source

enumFromThen :: And a -> And a -> [And a] Source

enumFromTo :: And a -> And a -> [And a] Source

enumFromThenTo :: And a -> And a -> And a -> [And a] Source

Enum a => Enum (Iff a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

succ :: Iff a -> Iff a Source

pred :: Iff a -> Iff a Source

toEnum :: Int -> Iff a Source

fromEnum :: Iff a -> Int Source

enumFrom :: Iff a -> [Iff a] Source

enumFromThen :: Iff a -> Iff a -> [Iff a] Source

enumFromTo :: Iff a -> Iff a -> [Iff a] Source

enumFromThenTo :: Iff a -> Iff a -> Iff a -> [Iff a] Source

Enum a => Enum (Ior a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

succ :: Ior a -> Ior a Source

pred :: Ior a -> Ior a Source

toEnum :: Int -> Ior a Source

fromEnum :: Ior a -> Int Source

enumFrom :: Ior a -> [Ior a] Source

enumFromThen :: Ior a -> Ior a -> [Ior a] Source

enumFromTo :: Ior a -> Ior a -> [Ior a] Source

enumFromThenTo :: Ior a -> Ior a -> Ior a -> [Ior a] Source

Enum a => Enum (Xor a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

succ :: Xor a -> Xor a Source

pred :: Xor a -> Xor a Source

toEnum :: Int -> Xor a Source

fromEnum :: Xor a -> Int Source

enumFrom :: Xor a -> [Xor a] Source

enumFromThen :: Xor a -> Xor a -> [Xor a] Source

enumFromTo :: Xor a -> Xor a -> [Xor a] Source

enumFromThenTo :: Xor a -> Xor a -> Xor a -> [Xor a] Source

Enum a => Enum (Identity a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

(Enum a, Bounded a, Eq a) => Enum (Down a) Source

Swaps succ and pred of the underlying type.

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

succ :: Down a -> Down a Source

pred :: Down a -> Down a Source

toEnum :: Int -> Down a Source

fromEnum :: Down a -> Int Source

enumFrom :: Down a -> [Down a] Source

enumFromThen :: Down a -> Down a -> [Down a] Source

enumFromTo :: Down a -> Down a -> [Down a] Source

enumFromThenTo :: Down a -> Down a -> Down a -> [Down a] Source

Integral a => Enum (Ratio a) Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Methods

succ :: Ratio a -> Ratio a Source

pred :: Ratio a -> Ratio a Source

toEnum :: Int -> Ratio a Source

fromEnum :: Ratio a -> Int Source

enumFrom :: Ratio a -> [Ratio a] Source

enumFromThen :: Ratio a -> Ratio a -> [Ratio a] Source

enumFromTo :: Ratio a -> Ratio a -> [Ratio a] Source

enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] Source

Enum a => Enum (Solo a) Source
Instance details

Defined in GHC.Internal.Enum

Methods

succ :: Solo a -> Solo a Source

pred :: Solo a -> Solo a Source

toEnum :: Int -> Solo a Source

fromEnum :: Solo a -> Int Source

enumFrom :: Solo a -> [Solo a] Source

enumFromThen :: Solo a -> Solo a -> [Solo a] Source

enumFromTo :: Solo a -> Solo a -> [Solo a] Source

enumFromThenTo :: Solo a -> Solo a -> Solo a -> [Solo a] Source

Enum (Fixed a) Source

Recall that, for numeric types, succ and pred typically add and subtract 1, respectively. This is not true in the case of Fixed, whose successor and predecessor functions intuitively return the "next" and "previous" values in the enumeration. The results of these functions thus depend on the resolution of the Fixed value. For example, when enumerating values of resolution 10^-3 of type Milli = Fixed E3,

>>> succ (0.000 :: Milli)
0.001

and likewise

>>> pred (0.000 :: Milli)
-0.001

In other words, succ and pred increment and decrement a fixed-precision value by the least amount such that the value's resolution is unchanged. For example, 10^-12 is the smallest (positive) amount that can be added to a value of type Pico = Fixed E12 without changing its resolution, and so

>>> succ (0.000000000000 :: Pico)
0.000000000001

and similarly

>>> pred (0.000000000000 :: Pico)
-0.000000000001

This is worth bearing in mind when defining Fixed arithmetic sequences. In particular, you may be forgiven for thinking the sequence

  [1..10] :: [Pico]

evaluates to [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] :: [Pico].

However, this is not true. On the contrary, similarly to the above implementations of succ and pred, enumFromTo :: Pico -> Pico -> [Pico] has a "step size" of 10^-12. Hence, the list [1..10] :: [Pico] has the form

  [1.000000000000, 1.00000000001, 1.00000000002, ..., 10.000000000000]

and contains 9 * 10^12 + 1 values.

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

succ :: Fixed a -> Fixed a Source

pred :: Fixed a -> Fixed a Source

toEnum :: Int -> Fixed a Source

fromEnum :: Fixed a -> Int Source

enumFrom :: Fixed a -> [Fixed a] Source

enumFromThen :: Fixed a -> Fixed a -> [Fixed a] Source

enumFromTo :: Fixed a -> Fixed a -> [Fixed a] Source

enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a] Source

Enum (Proxy s) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

succ :: Proxy s -> Proxy s Source

pred :: Proxy s -> Proxy s Source

toEnum :: Int -> Proxy s Source

fromEnum :: Proxy s -> Int Source

enumFrom :: Proxy s -> [Proxy s] Source

enumFromThen :: Proxy s -> Proxy s -> [Proxy s] Source

enumFromTo :: Proxy s -> Proxy s -> [Proxy s] Source

enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s] Source

Enum a => Enum (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

succ :: Const a b -> Const a b Source

pred :: Const a b -> Const a b Source

toEnum :: Int -> Const a b Source

fromEnum :: Const a b -> Int Source

enumFrom :: Const a b -> [Const a b] Source

enumFromThen :: Const a b -> Const a b -> [Const a b] Source

enumFromTo :: Const a b -> Const a b -> [Const a b] Source

enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] Source

Enum (f a) => Enum (Ap f a) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

succ :: Ap f a -> Ap f a Source

pred :: Ap f a -> Ap f a Source

toEnum :: Int -> Ap f a Source

fromEnum :: Ap f a -> Int Source

enumFrom :: Ap f a -> [Ap f a] Source

enumFromThen :: Ap f a -> Ap f a -> [Ap f a] Source

enumFromTo :: Ap f a -> Ap f a -> [Ap f a] Source

enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] Source

Enum (f a) => Enum (Alt f a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

succ :: Alt f a -> Alt f a Source

pred :: Alt f a -> Alt f a Source

toEnum :: Int -> Alt f a Source

fromEnum :: Alt f a -> Int Source

enumFrom :: Alt f a -> [Alt f a] Source

enumFromThen :: Alt f a -> Alt f a -> [Alt f a] Source

enumFromTo :: Alt f a -> Alt f a -> [Alt f a] Source

enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] Source

Coercible a b => Enum (Coercion a b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Coercion

Methods

succ :: Coercion a b -> Coercion a b Source

pred :: Coercion a b -> Coercion a b Source

toEnum :: Int -> Coercion a b Source

fromEnum :: Coercion a b -> Int Source

enumFrom :: Coercion a b -> [Coercion a b] Source

enumFromThen :: Coercion a b -> Coercion a b -> [Coercion a b] Source

enumFromTo :: Coercion a b -> Coercion a b -> [Coercion a b] Source

enumFromThenTo :: Coercion a b -> Coercion a b -> Coercion a b -> [Coercion a b] Source

a ~ b => Enum (a :~: b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

Methods

succ :: (a :~: b) -> a :~: b Source

pred :: (a :~: b) -> a :~: b Source

toEnum :: Int -> a :~: b Source

fromEnum :: (a :~: b) -> Int Source

enumFrom :: (a :~: b) -> [a :~: b] Source

enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b] Source

enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b] Source

enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b] Source

a ~~ b => Enum (a :~~: b) Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

Methods

succ :: (a :~~: b) -> a :~~: b Source

pred :: (a :~~: b) -> a :~~: b Source

toEnum :: Int -> a :~~: b Source

fromEnum :: (a :~~: b) -> Int Source

enumFrom :: (a :~~: b) -> [a :~~: b] Source

enumFromThen :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] Source

enumFromTo :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] Source

enumFromThenTo :: (a :~~: b) -> (a :~~: b) -> (a :~~: b) -> [a :~~: b] Source

Enum (f (g a)) => Enum (Compose f g a) Source

Since: base-4.19.0.0

Instance details

Defined in Data.Functor.Compose

Methods

succ :: Compose f g a -> Compose f g a Source

pred :: Compose f g a -> Compose f g a Source

toEnum :: Int -> Compose f g a Source

fromEnum :: Compose f g a -> Int Source

enumFrom :: Compose f g a -> [Compose f g a] Source

enumFromThen :: Compose f g a -> Compose f g a -> [Compose f g a] Source

enumFromTo :: Compose f g a -> Compose f g a -> [Compose f g a] Source

enumFromThenTo :: Compose f g a -> Compose f g a -> Compose f g a -> [Compose f g a] Source

class Bounded a where Source

The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds.

The Bounded class may be derived for any enumeration type; minBound is the first constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded.

Methods

minBound :: a Source

maxBound :: a Source

Instances
Instances details
Bounded ByteOrder Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.ByteOrder

Bounded All Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Bounded Any Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Bounded CBool Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CLLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CPtrdiff Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CSChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CSigAtomic Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CSize Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CUChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CUInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CUIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CUIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CULLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CULong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CUShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded CWchar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Bounded IntPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Bounded WordPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Bounded Associativity Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Bounded DecidedStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Bounded SourceStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Bounded SourceUnpackedness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Bounded Int16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Bounded Int32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Bounded Int64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Bounded Int8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Bounded Extension Source
Instance details

Defined in GHC.Internal.LanguageExtensions

Bounded CBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CBlkSize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CClockId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CDev Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CFsBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CFsFilCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CGid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CIno Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CKey Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CMode Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CNfds Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CNlink Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded COff Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CPid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CRLim Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CSocklen Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CSsize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CTcflag Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded CUid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded Fd Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Bounded GeneralCategory Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Unicode

Bounded Word16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Bounded Word32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Bounded Word64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Bounded Word8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Bounded Ordering Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Bounded () Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: () Source

maxBound :: () Source

Bounded Bool Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Bounded Char Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Bounded Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Bounded Levity Source

Since: base-4.16.0.0

Instance details

Defined in GHC.Internal.Enum

Bounded VecCount Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Enum

Bounded VecElem Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Enum

Bounded Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Bounded a => Bounded (First a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Bounded a => Bounded (Last a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Last a Source

maxBound :: Last a Source

Bounded a => Bounded (Max a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Max a Source

maxBound :: Max a Source

Bounded a => Bounded (Min a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Min a Source

maxBound :: Min a Source

Bounded m => Bounded (WrappedMonoid m) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Bounded a => Bounded (And a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

minBound :: And a Source

maxBound :: And a Source

Bounded a => Bounded (Iff a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

minBound :: Iff a Source

maxBound :: Iff a Source

Bounded a => Bounded (Ior a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

minBound :: Ior a Source

maxBound :: Ior a Source

Bounded a => Bounded (Xor a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

minBound :: Xor a Source

maxBound :: Xor a Source

Bounded a => Bounded (Identity a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Bounded a => Bounded (Down a) Source

Swaps minBound and maxBound of the underlying type.

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

minBound :: Down a Source

maxBound :: Down a Source

Bounded a => Bounded (Dual a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Dual a Source

maxBound :: Dual a Source

Bounded a => Bounded (Product a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Bounded a => Bounded (Sum a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Sum a Source

maxBound :: Sum a Source

Bounded a => Bounded (Solo a) Source
Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: Solo a Source

maxBound :: Solo a Source

Bounded (Proxy t) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

(Bounded a, Bounded b) => Bounded (a, b) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b) Source

maxBound :: (a, b) Source

Bounded a => Bounded (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

minBound :: Const a b Source

maxBound :: Const a b Source

(Applicative f, Bounded a) => Bounded (Ap f a) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

minBound :: Ap f a Source

maxBound :: Ap f a Source

Coercible a b => Bounded (Coercion a b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Coercion

a ~ b => Bounded (a :~: b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

Methods

minBound :: a :~: b Source

maxBound :: a :~: b Source

(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c) Source

maxBound :: (a, b, c) Source

a ~~ b => Bounded (a :~~: b) Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

Methods

minBound :: a :~~: b Source

maxBound :: a :~~: b Source

(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d) Source

maxBound :: (a, b, c, d) Source

Bounded (f (g a)) => Bounded (Compose f g a) Source

Since: base-4.19.0.0

Instance details

Defined in Data.Functor.Compose

Methods

minBound :: Compose f g a Source

maxBound :: Compose f g a Source

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d, e) Source

maxBound :: (a, b, c, d, e) Source

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d, e, f) Source

maxBound :: (a, b, c, d, e, f) Source

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d, e, f, g) Source

maxBound :: (a, b, c, d, e, f, g) Source

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h) Source

maxBound :: (a, b, c, d, e, f, g, h) Source

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i) Source

maxBound :: (a, b, c, d, e, f, g, h, i) Source

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j) Source

maxBound :: (a, b, c, d, e, f, g, h, i, j) Source

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k) Source

maxBound :: (a, b, c, d, e, f, g, h, i, j, k) Source

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l) Source

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l) Source

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) Source

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) Source

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source

Numbers

Numeric types

data Int Source

A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class.

Instances
Instances details
PrintfArg Int Source

Since: base-2.1

Instance details

Defined in Text.Printf

Bits Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Bits

FiniteBits Int Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Bits

Data Int Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int -> c Int Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int Source

toConstr :: Int -> Constr Source

dataTypeOf :: Int -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int) Source

gmapT :: (forall b. Data b => b -> b) -> Int -> Int Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Int -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Int -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int -> m Int Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int Source

Bounded Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Enum Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Storable Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Foreign.Storable

Methods

sizeOf :: Int -> Int Source

alignment :: Int -> Int Source

peekElemOff :: Ptr Int -> Int -> IO Int Source

pokeElemOff :: Ptr Int -> Int -> Int -> IO () Source

peekByteOff :: Ptr b -> Int -> IO Int Source

pokeByteOff :: Ptr b -> Int -> Int -> IO () Source

peek :: Ptr Int -> IO Int Source

poke :: Ptr Int -> Int -> IO () Source

Ix Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Ix

Methods

range :: (Int, Int) -> [Int] Source

index :: (Int, Int) -> Int -> Int Source

unsafeIndex :: (Int, Int) -> Int -> Int Source

inRange :: (Int, Int) -> Int -> Bool Source

rangeSize :: (Int, Int) -> Int Source

unsafeRangeSize :: (Int, Int) -> Int Source

Num Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Num

Methods

(+) :: Int -> Int -> Int Source

(-) :: Int -> Int -> Int Source

(*) :: Int -> Int -> Int Source

negate :: Int -> Int Source

abs :: Int -> Int Source

signum :: Int -> Int Source

fromInteger :: Integer -> Int Source

Read Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Integral Int Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Methods

quot :: Int -> Int -> Int Source

rem :: Int -> Int -> Int Source

div :: Int -> Int -> Int Source

mod :: Int -> Int -> Int Source

quotRem :: Int -> Int -> (Int, Int) Source

divMod :: Int -> Int -> (Int, Int) Source

toInteger :: Int -> Integer Source

Real Int Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Methods

toRational :: Int -> Rational Source

Show Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> Int -> ShowS Source

show :: Int -> String Source

showList :: [Int] -> ShowS Source

Eq Int Source
Instance details

Defined in GHC.Classes

Methods

(==) :: Int -> Int -> Bool Source

(/=) :: Int -> Int -> Bool Source

Ord Int Source
Instance details

Defined in GHC.Classes

Methods

compare :: Int -> Int -> Ordering Source

(<) :: Int -> Int -> Bool Source

(<=) :: Int -> Int -> Bool Source

(>) :: Int -> Int -> Bool Source

(>=) :: Int -> Int -> Bool Source

max :: Int -> Int -> Int Source

min :: Int -> Int -> Int Source

Lift Int Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Int -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Int -> Code m Int Source

Generic1 (URec Int :: k -> Type) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 (URec Int :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Int :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: k -> Type)))

Methods

from1 :: forall (a :: k). URec Int a -> Rep1 (URec Int :: k -> Type) a Source

to1 :: forall (a :: k). Rep1 (URec Int :: k -> Type) a -> URec Int a Source

Eq1 (UInt :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> UInt a -> UInt b -> Bool Source

Ord1 (UInt :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> UInt a -> UInt b -> Ordering Source

Show1 (UInt :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> UInt a -> ShowS Source

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [UInt a] -> ShowS Source

Foldable (UInt :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UInt m -> m Source

foldMap :: Monoid m => (a -> m) -> UInt a -> m Source

foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source

foldr :: (a -> b -> b) -> b -> UInt a -> b Source

foldr' :: (a -> b -> b) -> b -> UInt a -> b Source

foldl :: (b -> a -> b) -> b -> UInt a -> b Source

foldl' :: (b -> a -> b) -> b -> UInt a -> b Source

foldr1 :: (a -> a -> a) -> UInt a -> a Source

foldl1 :: (a -> a -> a) -> UInt a -> a Source

toList :: UInt a -> [a] Source

null :: UInt a -> Bool Source

length :: UInt a -> Int Source

elem :: Eq a => a -> UInt a -> Bool Source

maximum :: Ord a => UInt a -> a Source

minimum :: Ord a => UInt a -> a Source

sum :: Num a => UInt a -> a Source

product :: Num a => UInt a -> a Source

Traversable (UInt :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UInt a -> f (UInt b) Source

sequenceA :: Applicative f => UInt (f a) -> f (UInt a) Source

mapM :: Monad m => (a -> m b) -> UInt a -> m (UInt b) Source

sequence :: Monad m => UInt (m a) -> m (UInt a) Source

Functor (URec Int :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Int a -> URec Int b Source

(<$) :: a -> URec Int b -> URec Int a Source

Generic (URec Int p) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (URec Int p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: Type -> Type)))

Methods

from :: URec Int p -> Rep (URec Int p) x Source

to :: Rep (URec Int p) x -> URec Int p Source

Show (URec Int p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> URec Int p -> ShowS Source

show :: URec Int p -> String Source

showList :: [URec Int p] -> ShowS Source

Eq (URec Int p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Int p -> URec Int p -> Bool Source

(/=) :: URec Int p -> URec Int p -> Bool Source

Ord (URec Int p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: URec Int p -> URec Int p -> Ordering Source

(<) :: URec Int p -> URec Int p -> Bool Source

(<=) :: URec Int p -> URec Int p -> Bool Source

(>) :: URec Int p -> URec Int p -> Bool Source

(>=) :: URec Int p -> URec Int p -> Bool Source

max :: URec Int p -> URec Int p -> URec Int p Source

min :: URec Int p -> URec Int p -> URec Int p Source

data URec Int (p :: k) Source

Used for marking occurrences of Int#

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

data URec Int (p :: k) = UInt {}
type Rep1 (URec Int :: k -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Int :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: k -> Type)))
type Rep (URec Int p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (URec Int p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: Type -> Type)))

data Integer

Instances
Instances details
PrintfArg Integer Source

Since: base-2.1

Instance details

Defined in Text.Printf

Bits Integer Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Bits

Data Integer Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Integer -> c Integer Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Integer Source

toConstr :: Integer -> Constr Source

dataTypeOf :: Integer -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Integer) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Integer) Source

gmapT :: (forall b. Data b => b -> b) -> Integer -> Integer Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Integer -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Integer -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source

Enum Integer Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Ix Integer Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Ix

Num Integer Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Num

Read Integer Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Integral Integer Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Real Integer Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Show Integer Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Eq Integer
Instance details

Defined in GHC.Num.Integer

Ord Integer
Instance details

Defined in GHC.Num.Integer

Lift Integer Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Integer -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Integer -> Code m Integer Source

data Float Source

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Instances
Instances details
PrintfArg Float Source

Since: base-2.1

Instance details

Defined in Text.Printf

Data Float Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Float -> c Float Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Float Source

toConstr :: Float -> Constr Source

dataTypeOf :: Float -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Float) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Float) Source

gmapT :: (forall b. Data b => b -> b) -> Float -> Float Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Float -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Float -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Float -> m Float Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source

Floating Float Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

RealFloat Float Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Storable Float Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Foreign.Storable

Read Float Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Eq Float Source

Note that due to the presence of NaN, Float's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Float)
False

Also note that Float's Eq instance does not satisfy extensionality:

>>> 0 == (-0 :: Float)
True
>>> recip 0 == recip (-0 :: Float)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Float -> Float -> Bool Source

(/=) :: Float -> Float -> Bool Source

Ord Float Source

See instance Ord Double for discussion of deviations from IEEE 754 standard.

Instance details

Defined in GHC.Classes

Lift Float Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Float -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Float -> Code m Float Source

Generic1 (URec Float :: k -> Type) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 (URec Float :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Float :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: k -> Type)))

Methods

from1 :: forall (a :: k). URec Float a -> Rep1 (URec Float :: k -> Type) a Source

to1 :: forall (a :: k). Rep1 (URec Float :: k -> Type) a -> URec Float a Source

Eq1 (UFloat :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> UFloat a -> UFloat b -> Bool Source

Ord1 (UFloat :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> UFloat a -> UFloat b -> Ordering Source

Show1 (UFloat :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> UFloat a -> ShowS Source

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [UFloat a] -> ShowS Source

Foldable (UFloat :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UFloat m -> m Source

foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source

foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source

foldr :: (a -> b -> b) -> b -> UFloat a -> b Source

foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source

foldl :: (b -> a -> b) -> b -> UFloat a -> b Source

foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source

foldr1 :: (a -> a -> a) -> UFloat a -> a Source

foldl1 :: (a -> a -> a) -> UFloat a -> a Source

toList :: UFloat a -> [a] Source

null :: UFloat a -> Bool Source

length :: UFloat a -> Int Source

elem :: Eq a => a -> UFloat a -> Bool Source

maximum :: Ord a => UFloat a -> a Source

minimum :: Ord a => UFloat a -> a Source

sum :: Num a => UFloat a -> a Source

product :: Num a => UFloat a -> a Source

Traversable (UFloat :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UFloat a -> f (UFloat b) Source

sequenceA :: Applicative f => UFloat (f a) -> f (UFloat a) Source

mapM :: Monad m => (a -> m b) -> UFloat a -> m (UFloat b) Source

sequence :: Monad m => UFloat (m a) -> m (UFloat a) Source

Functor (URec Float :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Float a -> URec Float b Source

(<$) :: a -> URec Float b -> URec Float a Source

Generic (URec Float p) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (URec Float p)
Instance details

Defined in GHC.Internal.Generics

type Rep (URec Float p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: Type -> Type)))

Methods

from :: URec Float p -> Rep (URec Float p) x Source

to :: Rep (URec Float p) x -> URec Float p Source

Show (URec Float p) Source
Instance details

Defined in GHC.Internal.Generics

Eq (URec Float p) Source
Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Float p -> URec Float p -> Bool Source

(/=) :: URec Float p -> URec Float p -> Bool Source

Ord (URec Float p) Source
Instance details

Defined in GHC.Internal.Generics

data URec Float (p :: k) Source

Used for marking occurrences of Float#

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

data URec Float (p :: k) = UFloat {}
type Rep1 (URec Float :: k -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Float :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: k -> Type)))
type Rep (URec Float p) Source
Instance details

Defined in GHC.Internal.Generics

type Rep (URec Float p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: Type -> Type)))

data Double Source

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Instances
Instances details
PrintfArg Double Source

Since: base-2.1

Instance details

Defined in Text.Printf

Data Double Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Double -> c Double Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Double Source

toConstr :: Double -> Constr Source

dataTypeOf :: Double -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Double) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Double) Source

gmapT :: (forall b. Data b => b -> b) -> Double -> Double Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Double -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Double -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Double -> m Double Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source

Floating Double Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

RealFloat Double Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Storable Double Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Foreign.Storable

Read Double Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Eq Double Source

Note that due to the presence of NaN, Double's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Double)
False

Also note that Double's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Double)
True
>>> recip 0 == recip (-0 :: Double)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Double -> Double -> Bool Source

(/=) :: Double -> Double -> Bool Source

Ord Double Source

IEEE 754 Double-precision type includes not only numbers, but also positive and negative infinities and a special element called NaN (which can be quiet or signal).

IEEE 754-2008, section 5.11 requires that if at least one of arguments of <=, <, >, >= is NaN then the result of the comparison is False, and instance Ord Double complies with this requirement. This violates the reflexivity: both NaN <= NaN and NaN >= NaN are False.

IEEE 754-2008, section 5.10 defines totalOrder predicate. Unfortunately, compare on Doubles violates the IEEE standard and does not define a total order. More specifically, both compare NaN x and compare x NaN always return GT.

Thus, users must be extremely cautious when using instance Ord Double. For instance, one should avoid ordered containers with keys represented by Double, because data loss and corruption may happen. An IEEE-compliant compare is available in fp-ieee package as TotallyOrdered newtype.

Moving further, the behaviour of min and max with regards to NaN is also non-compliant. IEEE 754-2008, section 5.3.1 defines that quiet NaN should be treated as a missing data by minNum and maxNum functions, for example, minNum(NaN, 1) = minNum(1, NaN) = 1. Some languages such as Java deviate from the standard implementing minNum(NaN, 1) = minNum(1, NaN) = NaN. However, min / max in base are even worse: min NaN 1 is 1, but min 1 NaN is NaN.

IEEE 754-2008 compliant min / max can be found in ieee754 package under minNum / maxNum names. Implementations compliant with minimumNumber / maximumNumber from a newer IEEE 754-2019, section 9.6 are available from fp-ieee package.

Instance details

Defined in GHC.Classes

Lift Double Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Double -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Double -> Code m Double Source

Generic1 (URec Double :: k -> Type) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 (URec Double :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: k -> Type)))

Methods

from1 :: forall (a :: k). URec Double a -> Rep1 (URec Double :: k -> Type) a Source

to1 :: forall (a :: k). Rep1 (URec Double :: k -> Type) a -> URec Double a Source

Eq1 (UDouble :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> UDouble a -> UDouble b -> Bool Source

Ord1 (UDouble :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> UDouble a -> UDouble b -> Ordering Source

Show1 (UDouble :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> UDouble a -> ShowS Source

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [UDouble a] -> ShowS Source

Foldable (UDouble :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UDouble m -> m Source

foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source

foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source

foldr :: (a -> b -> b) -> b -> UDouble a -> b Source

foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source

foldl :: (b -> a -> b) -> b -> UDouble a -> b Source

foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source

foldr1 :: (a -> a -> a) -> UDouble a -> a Source

foldl1 :: (a -> a -> a) -> UDouble a -> a Source

toList :: UDouble a -> [a] Source

null :: UDouble a -> Bool Source

length :: UDouble a -> Int Source

elem :: Eq a => a -> UDouble a -> Bool Source

maximum :: Ord a => UDouble a -> a Source

minimum :: Ord a => UDouble a -> a Source

sum :: Num a => UDouble a -> a Source

product :: Num a => UDouble a -> a Source

Traversable (UDouble :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b) Source

sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a) Source

mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b) Source

sequence :: Monad m => UDouble (m a) -> m (UDouble a) Source

Functor (URec Double :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b Source

(<$) :: a -> URec Double b -> URec Double a Source

Generic (URec Double p) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

Methods

from :: URec Double p -> Rep (URec Double p) x Source

to :: Rep (URec Double p) x -> URec Double p Source

Show (URec Double p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Eq (URec Double p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Double p -> URec Double p -> Bool Source

(/=) :: URec Double p -> URec Double p -> Bool Source

Ord (URec Double p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

data URec Double (p :: k) Source

Used for marking occurrences of Double#

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

data URec Double (p :: k) = UDouble {}
type Rep1 (URec Double :: k -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: k -> Type)))
type Rep (URec Double p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

type Rational = Ratio Integer Source

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

data Word Source

A Word is an unsigned integral type, with the same size as Int.

Instances
Instances details
PrintfArg Word Source

Since: base-2.1

Instance details

Defined in Text.Printf

Bits Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Bits

FiniteBits Word Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Bits

Data Word Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word -> c Word Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word Source

toConstr :: Word -> Constr Source

dataTypeOf :: Word -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word) Source

gmapT :: (forall b. Data b => b -> b) -> Word -> Word Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Word -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Word -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word -> m Word Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word Source

Bounded Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Enum Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Enum

Storable Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Foreign.Storable

Ix Word Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Ix

Num Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Num

Read Word Source

Since: base-4.5.0.0

Instance details

Defined in GHC.Internal.Read

Integral Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Real

Real Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Real

Methods

toRational :: Word -> Rational Source

Show Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Eq Word Source
Instance details

Defined in GHC.Classes

Methods

(==) :: Word -> Word -> Bool Source

(/=) :: Word -> Word -> Bool Source

Ord Word Source
Instance details

Defined in GHC.Classes

Methods

compare :: Word -> Word -> Ordering Source

(<) :: Word -> Word -> Bool Source

(<=) :: Word -> Word -> Bool Source

(>) :: Word -> Word -> Bool Source

(>=) :: Word -> Word -> Bool Source

max :: Word -> Word -> Word Source

min :: Word -> Word -> Word Source

Lift Word Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Word -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Word -> Code m Word Source

Generic1 (URec Word :: k -> Type) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 (URec Word :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Word :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: k -> Type)))

Methods

from1 :: forall (a :: k). URec Word a -> Rep1 (URec Word :: k -> Type) a Source

to1 :: forall (a :: k). Rep1 (URec Word :: k -> Type) a -> URec Word a Source

Eq1 (UWord :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> UWord a -> UWord b -> Bool Source

Ord1 (UWord :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> UWord a -> UWord b -> Ordering Source

Show1 (UWord :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> UWord a -> ShowS Source

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [UWord a] -> ShowS Source

Foldable (UWord :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UWord m -> m Source

foldMap :: Monoid m => (a -> m) -> UWord a -> m Source

foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source

foldr :: (a -> b -> b) -> b -> UWord a -> b Source

foldr' :: (a -> b -> b) -> b -> UWord a -> b Source

foldl :: (b -> a -> b) -> b -> UWord a -> b Source

foldl' :: (b -> a -> b) -> b -> UWord a -> b Source

foldr1 :: (a -> a -> a) -> UWord a -> a Source

foldl1 :: (a -> a -> a) -> UWord a -> a Source

toList :: UWord a -> [a] Source

null :: UWord a -> Bool Source

length :: UWord a -> Int Source

elem :: Eq a => a -> UWord a -> Bool Source

maximum :: Ord a => UWord a -> a Source

minimum :: Ord a => UWord a -> a Source

sum :: Num a => UWord a -> a Source

product :: Num a => UWord a -> a Source

Traversable (UWord :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UWord a -> f (UWord b) Source

sequenceA :: Applicative f => UWord (f a) -> f (UWord a) Source

mapM :: Monad m => (a -> m b) -> UWord a -> m (UWord b) Source

sequence :: Monad m => UWord (m a) -> m (UWord a) Source

Functor (URec Word :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Word a -> URec Word b Source

(<$) :: a -> URec Word b -> URec Word a Source

Generic (URec Word p) Source
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (URec Word p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: Type -> Type)))

Methods

from :: URec Word p -> Rep (URec Word p) x Source

to :: Rep (URec Word p) x -> URec Word p Source

Show (URec Word p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Eq (URec Word p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Word p -> URec Word p -> Bool Source

(/=) :: URec Word p -> URec Word p -> Bool Source

Ord (URec Word p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: URec Word p -> URec Word p -> Ordering Source

(<) :: URec Word p -> URec Word p -> Bool Source

(<=) :: URec Word p -> URec Word p -> Bool Source

(>) :: URec Word p -> URec Word p -> Bool Source

(>=) :: URec Word p -> URec Word p -> Bool Source

max :: URec Word p -> URec Word p -> URec Word p Source

min :: URec Word p -> URec Word p -> URec Word p Source

data URec Word (p :: k) Source

Used for marking occurrences of Word#

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

data URec Word (p :: k) = UWord {}
type Rep1 (URec Word :: k -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Word :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: k -> Type)))
type Rep (URec Word p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (URec Word p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: Type -> Type)))

Numeric type classes

class Num a where Source

Basic numeric class.

The Haskell Report defines no laws for Num. However, (+) and (*) are customarily expected to define a ring and have the following properties:

Associativity of (+)
(x + y) + z = x + (y + z)
Commutativity of (+)
x + y = y + x
fromInteger 0 is the additive identity
x + fromInteger 0 = x
negate gives the additive inverse
x + negate x = fromInteger 0
Associativity of (*)
(x * y) * z = x * (y * z)
fromInteger 1 is the multiplicative identity
x * fromInteger 1 = x and fromInteger 1 * x = x
Distributivity of (*) with respect to (+)
a * (b + c) = (a * b) + (a * c) and (b + c) * a = (b * a) + (c * a)
Coherence with toInteger
if the type also implements Integral, then fromInteger is a left inverse for toInteger, i.e. fromInteger (toInteger i) == i

Note that it isn't customarily expected that a type instance of both Num and Ord implement an ordered ring. Indeed, in base only Integer and Rational do.

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

(+) :: a -> a -> a infixl 6 Source

(-) :: a -> a -> a infixl 6 Source

(*) :: a -> a -> a infixl 7 Source

negate :: a -> a Source

Unary negation.

abs :: a -> a Source

Absolute value.

signum :: a -> a Source

Sign of a number. The functions abs and signum should satisfy the law:

abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

fromInteger :: Integer -> a Source

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

Instances
Instances details
Num Unique Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Unique

Methods

(+) :: Unique -> Unique -> Unique Source

(-) :: Unique -> Unique -> Unique Source

(*) :: Unique -> Unique -> Unique Source

negate :: Unique -> Unique Source

abs :: Unique -> Unique Source

signum :: Unique -> Unique Source

fromInteger :: Integer -> Unique Source

Num CBool Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CClock Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CDouble Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CFloat Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CLLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CPtrdiff Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CSChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CSUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CSigAtomic Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CSize Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CTime Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CUChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CUInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CUIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CUIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CULLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CULong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CUShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num CWchar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Num IntPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Num WordPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Num Int16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Num Int32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Num Int64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Num Int8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Num CBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CBlkSize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CCc Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(+) :: CCc -> CCc -> CCc Source

(-) :: CCc -> CCc -> CCc Source

(*) :: CCc -> CCc -> CCc Source

negate :: CCc -> CCc Source

abs :: CCc -> CCc Source

signum :: CCc -> CCc Source

fromInteger :: Integer -> CCc Source

Num CClockId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CDev Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CFsBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CFsFilCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CGid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(+) :: CId -> CId -> CId Source

(-) :: CId -> CId -> CId Source

(*) :: CId -> CId -> CId Source

negate :: CId -> CId Source

abs :: CId -> CId Source

signum :: CId -> CId Source

fromInteger :: Integer -> CId Source

Num CIno Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CKey Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CMode Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CNfds Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CNlink Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num COff Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CPid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CRLim Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CSocklen Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CSpeed Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CSsize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CTcflag Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num CUid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Num Fd Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

(+) :: Fd -> Fd -> Fd Source

(-) :: Fd -> Fd -> Fd Source

(*) :: Fd -> Fd -> Fd Source

negate :: Fd -> Fd Source

abs :: Fd -> Fd Source

signum :: Fd -> Fd Source

fromInteger :: Integer -> Fd Source

Num Word16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Num Word32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Num Word64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Num Word8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Num Integer Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Num

Num Natural Source

Note that Natural's Num instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though.

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Num

Num Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Num

Methods

(+) :: Int -> Int -> Int Source

(-) :: Int -> Int -> Int Source

(*) :: Int -> Int -> Int Source

negate :: Int -> Int Source

abs :: Int -> Int Source

signum :: Int -> Int Source

fromInteger :: Integer -> Int Source

Num Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Num

RealFloat a => Num (Complex a) Source

Since: base-2.1

Instance details

Defined in Data.Complex

Num a => Num (Max a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(+) :: Max a -> Max a -> Max a Source

(-) :: Max a -> Max a -> Max a Source

(*) :: Max a -> Max a -> Max a Source

negate :: Max a -> Max a Source

abs :: Max a -> Max a Source

signum :: Max a -> Max a Source

fromInteger :: Integer -> Max a Source

Num a => Num (Min a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(+) :: Min a -> Min a -> Min a Source

(-) :: Min a -> Min a -> Min a Source

(*) :: Min a -> Min a -> Min a Source

negate :: Min a -> Min a Source

abs :: Min a -> Min a Source

signum :: Min a -> Min a Source

fromInteger :: Integer -> Min a Source

Num a => Num (Identity a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Num a => Num (Down a) Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

(+) :: Down a -> Down a -> Down a Source

(-) :: Down a -> Down a -> Down a Source

(*) :: Down a -> Down a -> Down a Source

negate :: Down a -> Down a Source

abs :: Down a -> Down a Source

signum :: Down a -> Down a Source

fromInteger :: Integer -> Down a Source

Num a => Num (Product a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Num a => Num (Sum a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(+) :: Sum a -> Sum a -> Sum a Source

(-) :: Sum a -> Sum a -> Sum a Source

(*) :: Sum a -> Sum a -> Sum a Source

negate :: Sum a -> Sum a Source

abs :: Sum a -> Sum a Source

signum :: Sum a -> Sum a Source

fromInteger :: Integer -> Sum a Source

Integral a => Num (Ratio a) Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Methods

(+) :: Ratio a -> Ratio a -> Ratio a Source

(-) :: Ratio a -> Ratio a -> Ratio a Source

(*) :: Ratio a -> Ratio a -> Ratio a Source

negate :: Ratio a -> Ratio a Source

abs :: Ratio a -> Ratio a Source

signum :: Ratio a -> Ratio a Source

fromInteger :: Integer -> Ratio a Source

HasResolution a => Num (Fixed a) Source

Multiplication is not associative or distributive:

>>> (0.2 * 0.6 :: Deci) * 0.9 == 0.2 * (0.6 * 0.9)
False
>>> (0.1 + 0.1 :: Deci) * 0.5 == 0.1 * 0.5 + 0.1 * 0.5
False

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

(+) :: Fixed a -> Fixed a -> Fixed a Source

(-) :: Fixed a -> Fixed a -> Fixed a Source

(*) :: Fixed a -> Fixed a -> Fixed a Source

negate :: Fixed a -> Fixed a Source

abs :: Fixed a -> Fixed a Source

signum :: Fixed a -> Fixed a Source

fromInteger :: Integer -> Fixed a Source

Num a => Num (Op a b) Source
Instance details

Defined in Data.Functor.Contravariant

Methods

(+) :: Op a b -> Op a b -> Op a b Source

(-) :: Op a b -> Op a b -> Op a b Source

(*) :: Op a b -> Op a b -> Op a b Source

negate :: Op a b -> Op a b Source

abs :: Op a b -> Op a b Source

signum :: Op a b -> Op a b Source

fromInteger :: Integer -> Op a b Source

Num a => Num (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

(+) :: Const a b -> Const a b -> Const a b Source

(-) :: Const a b -> Const a b -> Const a b Source

(*) :: Const a b -> Const a b -> Const a b Source

negate :: Const a b -> Const a b Source

abs :: Const a b -> Const a b Source

signum :: Const a b -> Const a b Source

fromInteger :: Integer -> Const a b Source

(Applicative f, Num a) => Num (Ap f a) Source

Note that even if the underlying Num and Applicative instances are lawful, for most Applicatives, this instance will not be lawful. If you use this instance with the list Applicative, the following customary laws will not hold:

Commutativity:

>>> Ap [10,20] + Ap [1,2]
Ap {getAp = [11,12,21,22]}
>>> Ap [1,2] + Ap [10,20]
Ap {getAp = [11,21,12,22]}

Additive inverse:

>>> Ap [] + negate (Ap [])
Ap {getAp = []}
>>> fromInteger 0 :: Ap [] Int
Ap {getAp = [0]}

Distributivity:

>>> Ap [1,2] * (3 + 4)
Ap {getAp = [7,14]}
>>> (Ap [1,2] * 3) + (Ap [1,2] * 4)
Ap {getAp = [7,11,10,14]}

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(+) :: Ap f a -> Ap f a -> Ap f a Source

(-) :: Ap f a -> Ap f a -> Ap f a Source

(*) :: Ap f a -> Ap f a -> Ap f a Source

negate :: Ap f a -> Ap f a Source

abs :: Ap f a -> Ap f a Source

signum :: Ap f a -> Ap f a Source

fromInteger :: Integer -> Ap f a Source

Num (f a) => Num (Alt f a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(+) :: Alt f a -> Alt f a -> Alt f a Source

(-) :: Alt f a -> Alt f a -> Alt f a Source

(*) :: Alt f a -> Alt f a -> Alt f a Source

negate :: Alt f a -> Alt f a Source

abs :: Alt f a -> Alt f a Source

signum :: Alt f a -> Alt f a Source

fromInteger :: Integer -> Alt f a Source

Num (f (g a)) => Num (Compose f g a) Source

Since: base-4.19.0.0

Instance details

Defined in Data.Functor.Compose

Methods

(+) :: Compose f g a -> Compose f g a -> Compose f g a Source

(-) :: Compose f g a -> Compose f g a -> Compose f g a Source

(*) :: Compose f g a -> Compose f g a -> Compose f g a Source

negate :: Compose f g a -> Compose f g a Source

abs :: Compose f g a -> Compose f g a Source

signum :: Compose f g a -> Compose f g a Source

fromInteger :: Integer -> Compose f g a Source

class (Num a, Ord a) => Real a where Source

Real numbers.

The Haskell report defines no laws for Real, however Real instances are customarily expected to adhere to the following law:

Coherence with fromRational
if the type also implements Fractional, then fromRational is a left inverse for toRational, i.e. fromRational (toRational i) = i

The law does not hold for Float, Double, CFloat, CDouble, etc., because these types contain non-finite values, which cannot be roundtripped through Rational.

Methods

toRational :: a -> Rational Source

Rational equivalent of its real argument with full precision.

Instances
Instances details
Real CBool Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CClock Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CDouble Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CFloat Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

toRational :: CInt -> Rational Source

Real CIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CLLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CPtrdiff Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CSChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CSUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CSigAtomic Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CSize Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CTime Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CUChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CUInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CUIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CUIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CULLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CULong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CUShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real CWchar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Real IntPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Real WordPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Real Int16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Real Int32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Real Int64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Real Int8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Methods

toRational :: Int8 -> Rational Source

Real CBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CBlkSize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CCc Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

toRational :: CCc -> Rational Source

Real CClockId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CDev Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

toRational :: CDev -> Rational Source

Real CFsBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CFsFilCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CGid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

toRational :: CGid -> Rational Source

Real CId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

toRational :: CId -> Rational Source

Real CIno Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

toRational :: CIno -> Rational Source

Real CKey Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

toRational :: CKey -> Rational Source

Real CMode Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CNfds Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CNlink Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real COff Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

toRational :: COff -> Rational Source

Real CPid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

toRational :: CPid -> Rational Source

Real CRLim Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CSocklen Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CSpeed Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CSsize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CTcflag Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Real CUid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

toRational :: CUid -> Rational Source

Real Fd Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

toRational :: Fd -> Rational Source

Real Word16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Real Word32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Real Word64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Real Word8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Real Integer Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Real Natural Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Real

Real Int Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Methods

toRational :: Int -> Rational Source

Real Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Real

Methods

toRational :: Word -> Rational Source

Real a => Real (Identity a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Real a => Real (Down a) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

toRational :: Down a -> Rational Source

Integral a => Real (Ratio a) Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Methods

toRational :: Ratio a -> Rational Source

HasResolution a => Real (Fixed a) Source

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

toRational :: Fixed a -> Rational Source

Real a => Real (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

toRational :: Const a b -> Rational Source

Real (f (g a)) => Real (Compose f g a) Source

Since: base-4.19.0.0

Instance details

Defined in Data.Functor.Compose

Methods

toRational :: Compose f g a -> Rational Source

class (Real a, Enum a) => Integral a where Source

Integral numbers, supporting integer division.

The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the div/mod and quot/rem pairs, given suitable Euclidean functions f and g:

An example of a suitable Euclidean function, for Integer's instance, is abs.

In addition, toInteger should be total, and fromInteger should be a left inverse for it, i.e. fromInteger (toInteger i) = i.

Minimal complete definition

quotRem, toInteger

Methods

quot :: a -> a -> a infixl 7 Source

Integer division truncated toward zero.

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

rem :: a -> a -> a infixl 7 Source

Integer remainder, satisfying

(x `quot` y)*y + (x `rem` y) == x

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

div :: a -> a -> a infixl 7 Source

Integer division truncated toward negative infinity.

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

mod :: a -> a -> a infixl 7 Source

Integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

quotRem :: a -> a -> (a, a) Source

Simultaneous quot and rem.

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

divMod :: a -> a -> (a, a) Source

simultaneous div and mod.

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

toInteger :: a -> Integer Source

Conversion to Integer.

Instances
Instances details
Integral CBool Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CLLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CPtrdiff Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CSChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CSigAtomic Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CSize Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CUChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CUInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CUIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CUIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CULLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CULong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CUShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral CWchar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Integral IntPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Integral WordPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Integral Int16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Integral Int32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Integral Int64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Integral Int8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Integral CBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CBlkSize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CClockId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CDev Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CFsBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CFsFilCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CGid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

quot :: CId -> CId -> CId Source

rem :: CId -> CId -> CId Source

div :: CId -> CId -> CId Source

mod :: CId -> CId -> CId Source

quotRem :: CId -> CId -> (CId, CId) Source

divMod :: CId -> CId -> (CId, CId) Source

toInteger :: CId -> Integer Source

Integral CIno Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CKey Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CMode Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CNfds Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CNlink Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral COff Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CPid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CRLim Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CSocklen Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CSsize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CTcflag Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral CUid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Integral Fd Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

quot :: Fd -> Fd -> Fd Source

rem :: Fd -> Fd -> Fd Source

div :: Fd -> Fd -> Fd Source

mod :: Fd -> Fd -> Fd Source

quotRem :: Fd -> Fd -> (Fd, Fd) Source

divMod :: Fd -> Fd -> (Fd, Fd) Source

toInteger :: Fd -> Integer Source

Integral Word16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Integral Word32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Integral Word64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Integral Word8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Integral Integer Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Integral Natural Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Real

Integral Int Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Methods

quot :: Int -> Int -> Int Source

rem :: Int -> Int -> Int Source

div :: Int -> Int -> Int Source

mod :: Int -> Int -> Int Source

quotRem :: Int -> Int -> (Int, Int) Source

divMod :: Int -> Int -> (Int, Int) Source

toInteger :: Int -> Integer Source

Integral Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Real

Integral a => Integral (Identity a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Integral a => Integral (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

quot :: Const a b -> Const a b -> Const a b Source

rem :: Const a b -> Const a b -> Const a b Source

div :: Const a b -> Const a b -> Const a b Source

mod :: Const a b -> Const a b -> Const a b Source

quotRem :: Const a b -> Const a b -> (Const a b, Const a b) Source

divMod :: Const a b -> Const a b -> (Const a b, Const a b) Source

toInteger :: Const a b -> Integer Source

Integral (f (g a)) => Integral (Compose f g a) Source

Since: base-4.19.0.0

Instance details

Defined in Data.Functor.Compose

Methods

quot :: Compose f g a -> Compose f g a -> Compose f g a Source

rem :: Compose f g a -> Compose f g a -> Compose f g a Source

div :: Compose f g a -> Compose f g a -> Compose f g a Source

mod :: Compose f g a -> Compose f g a -> Compose f g a Source

quotRem :: Compose f g a -> Compose f g a -> (Compose f g a, Compose f g a) Source

divMod :: Compose f g a -> Compose f g a -> (Compose f g a, Compose f g a) Source

toInteger :: Compose f g a -> Integer Source

class Num a => Fractional a where Source

Fractional numbers, supporting real division.

The Haskell Report defines no laws for Fractional. However, (+) and (*) are customarily expected to define a division ring and have the following properties:

recip gives the multiplicative inverse
x * recip x = recip x * x = fromInteger 1
Totality of toRational
toRational is total
Coherence with toRational
if the type also implements Real, then fromRational is a left inverse for toRational, i.e. fromRational (toRational i) = i

Note that it isn't customarily expected that a type instance of Fractional implement a field. However, all instances in base do.

Minimal complete definition

fromRational, (recip | (/))

Methods

(/) :: a -> a -> a infixl 7 Source

Fractional division.

recip :: a -> a Source

Reciprocal fraction.

fromRational :: Rational -> a Source

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

Instances
Instances details
Fractional CDouble Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Fractional CFloat Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

RealFloat a => Fractional (Complex a) Source

Since: base-2.1

Instance details

Defined in Data.Complex

Fractional a => Fractional (Identity a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Fractional a => Fractional (Down a) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

(/) :: Down a -> Down a -> Down a Source

recip :: Down a -> Down a Source

fromRational :: Rational -> Down a Source

Integral a => Fractional (Ratio a) Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Methods

(/) :: Ratio a -> Ratio a -> Ratio a Source

recip :: Ratio a -> Ratio a Source

fromRational :: Rational -> Ratio a Source

HasResolution a => Fractional (Fixed a) Source

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

(/) :: Fixed a -> Fixed a -> Fixed a Source

recip :: Fixed a -> Fixed a Source

fromRational :: Rational -> Fixed a Source

Fractional a => Fractional (Op a b) Source
Instance details

Defined in Data.Functor.Contravariant

Methods

(/) :: Op a b -> Op a b -> Op a b Source

recip :: Op a b -> Op a b Source

fromRational :: Rational -> Op a b Source

Fractional a => Fractional (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

(/) :: Const a b -> Const a b -> Const a b Source

recip :: Const a b -> Const a b Source

fromRational :: Rational -> Const a b Source

Fractional (f (g a)) => Fractional (Compose f g a) Source

Since: base-4.20.0.0

Instance details

Defined in Data.Functor.Compose

Methods

(/) :: Compose f g a -> Compose f g a -> Compose f g a Source

recip :: Compose f g a -> Compose f g a Source

fromRational :: Rational -> Compose f g a Source

class Fractional a => Floating a where Source

Trigonometric and hyperbolic functions and related functions.

The Haskell Report defines no laws for Floating. However, (+), (*) and exp are customarily expected to define an exponential field and have the following properties:

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a Source

exp :: a -> a Source

log :: a -> a Source

sqrt :: a -> a Source

(**) :: a -> a -> a infixr 8 Source

logBase :: a -> a -> a Source

sin :: a -> a Source

cos :: a -> a Source

tan :: a -> a Source

asin :: a -> a Source

acos :: a -> a Source

atan :: a -> a Source

sinh :: a -> a Source

cosh :: a -> a Source

tanh :: a -> a Source

asinh :: a -> a Source

acosh :: a -> a Source

atanh :: a -> a Source

Instances
Instances details
Floating CDouble Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Floating CFloat Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Floating Double Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Floating Float Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

RealFloat a => Floating (Complex a) Source

Since: base-2.1

Instance details

Defined in Data.Complex

Floating a => Floating (Identity a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Floating a => Floating (Down a) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

pi :: Down a Source

exp :: Down a -> Down a Source

log :: Down a -> Down a Source

sqrt :: Down a -> Down a Source

(**) :: Down a -> Down a -> Down a Source

logBase :: Down a -> Down a -> Down a Source

sin :: Down a -> Down a Source

cos :: Down a -> Down a Source

tan :: Down a -> Down a Source

asin :: Down a -> Down a Source

acos :: Down a -> Down a Source

atan :: Down a -> Down a Source

sinh :: Down a -> Down a Source

cosh :: Down a -> Down a Source

tanh :: Down a -> Down a Source

asinh :: Down a -> Down a Source

acosh :: Down a -> Down a Source

atanh :: Down a -> Down a Source

log1p :: Down a -> Down a Source

expm1 :: Down a -> Down a Source

log1pexp :: Down a -> Down a Source

log1mexp :: Down a -> Down a Source

Floating a => Floating (Op a b) Source
Instance details

Defined in Data.Functor.Contravariant

Methods

pi :: Op a b Source

exp :: Op a b -> Op a b Source

log :: Op a b -> Op a b Source

sqrt :: Op a b -> Op a b Source

(**) :: Op a b -> Op a b -> Op a b Source

logBase :: Op a b -> Op a b -> Op a b Source

sin :: Op a b -> Op a b Source

cos :: Op a b -> Op a b Source

tan :: Op a b -> Op a b Source

asin :: Op a b -> Op a b Source

acos :: Op a b -> Op a b Source

atan :: Op a b -> Op a b Source

sinh :: Op a b -> Op a b Source

cosh :: Op a b -> Op a b Source

tanh :: Op a b -> Op a b Source

asinh :: Op a b -> Op a b Source

acosh :: Op a b -> Op a b Source

atanh :: Op a b -> Op a b Source

log1p :: Op a b -> Op a b Source

expm1 :: Op a b -> Op a b Source

log1pexp :: Op a b -> Op a b Source

log1mexp :: Op a b -> Op a b Source

Floating a => Floating (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

pi :: Const a b Source

exp :: Const a b -> Const a b Source

log :: Const a b -> Const a b Source

sqrt :: Const a b -> Const a b Source

(**) :: Const a b -> Const a b -> Const a b Source

logBase :: Const a b -> Const a b -> Const a b Source

sin :: Const a b -> Const a b Source

cos :: Const a b -> Const a b Source

tan :: Const a b -> Const a b Source

asin :: Const a b -> Const a b Source

acos :: Const a b -> Const a b Source

atan :: Const a b -> Const a b Source

sinh :: Const a b -> Const a b Source

cosh :: Const a b -> Const a b Source

tanh :: Const a b -> Const a b Source

asinh :: Const a b -> Const a b Source

acosh :: Const a b -> Const a b Source

atanh :: Const a b -> Const a b Source

log1p :: Const a b -> Const a b Source

expm1 :: Const a b -> Const a b Source

log1pexp :: Const a b -> Const a b Source

log1mexp :: Const a b -> Const a b Source

Floating (f (g a)) => Floating (Compose f g a) Source

Since: base-4.20.0.0

Instance details

Defined in Data.Functor.Compose

Methods

pi :: Compose f g a Source

exp :: Compose f g a -> Compose f g a Source

log :: Compose f g a -> Compose f g a Source

sqrt :: Compose f g a -> Compose f g a Source

(**) :: Compose f g a -> Compose f g a -> Compose f g a Source

logBase :: Compose f g a -> Compose f g a -> Compose f g a Source

sin :: Compose f g a -> Compose f g a Source

cos :: Compose f g a -> Compose f g a Source

tan :: Compose f g a -> Compose f g a Source

asin :: Compose f g a -> Compose f g a Source

acos :: Compose f g a -> Compose f g a Source

atan :: Compose f g a -> Compose f g a Source

sinh :: Compose f g a -> Compose f g a Source

cosh :: Compose f g a -> Compose f g a Source

tanh :: Compose f g a -> Compose f g a Source

asinh :: Compose f g a -> Compose f g a Source

acosh :: Compose f g a -> Compose f g a Source

atanh :: Compose f g a -> Compose f g a Source

log1p :: Compose f g a -> Compose f g a Source

expm1 :: Compose f g a -> Compose f g a Source

log1pexp :: Compose f g a -> Compose f g a Source

log1mexp :: Compose f g a -> Compose f g a Source

class (Real a, Fractional a) => RealFrac a where Source

Extracting components of fractions.

Minimal complete definition

properFraction

Methods

properFraction :: Integral b => a -> (b, a) Source

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

truncate :: Integral b => a -> b Source

truncate x returns the integer nearest x between zero and x

round :: Integral b => a -> b Source

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

ceiling :: Integral b => a -> b Source

ceiling x returns the least integer not less than x

floor :: Integral b => a -> b Source

floor x returns the greatest integer not greater than x

Instances
Instances details
RealFrac CDouble Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

RealFrac CFloat Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

properFraction :: Integral b => CFloat -> (b, CFloat) Source

truncate :: Integral b => CFloat -> b Source

round :: Integral b => CFloat -> b Source

ceiling :: Integral b => CFloat -> b Source

floor :: Integral b => CFloat -> b Source

RealFrac a => RealFrac (Identity a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Methods

properFraction :: Integral b => Identity a -> (b, Identity a) Source

truncate :: Integral b => Identity a -> b Source

round :: Integral b => Identity a -> b Source

ceiling :: Integral b => Identity a -> b Source

floor :: Integral b => Identity a -> b Source

RealFrac a => RealFrac (Down a) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

properFraction :: Integral b => Down a -> (b, Down a) Source

truncate :: Integral b => Down a -> b Source

round :: Integral b => Down a -> b Source

ceiling :: Integral b => Down a -> b Source

floor :: Integral b => Down a -> b Source

Integral a => RealFrac (Ratio a) Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Methods

properFraction :: Integral b => Ratio a -> (b, Ratio a) Source

truncate :: Integral b => Ratio a -> b Source

round :: Integral b => Ratio a -> b Source

ceiling :: Integral b => Ratio a -> b Source

floor :: Integral b => Ratio a -> b Source

HasResolution a => RealFrac (Fixed a) Source

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

properFraction :: Integral b => Fixed a -> (b, Fixed a) Source

truncate :: Integral b => Fixed a -> b Source

round :: Integral b => Fixed a -> b Source

ceiling :: Integral b => Fixed a -> b Source

floor :: Integral b => Fixed a -> b Source

RealFrac a => RealFrac (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

properFraction :: Integral b0 => Const a b -> (b0, Const a b) Source

truncate :: Integral b0 => Const a b -> b0 Source

round :: Integral b0 => Const a b -> b0 Source

ceiling :: Integral b0 => Const a b -> b0 Source

floor :: Integral b0 => Const a b -> b0 Source

RealFrac (f (g a)) => RealFrac (Compose f g a) Source

Since: base-4.20.0.0

Instance details

Defined in Data.Functor.Compose

Methods

properFraction :: Integral b => Compose f g a -> (b, Compose f g a) Source

truncate :: Integral b => Compose f g a -> b Source

round :: Integral b => Compose f g a -> b Source

ceiling :: Integral b => Compose f g a -> b Source

floor :: Integral b => Compose f g a -> b Source

class (RealFrac a, Floating a) => RealFloat a where Source

Efficient, machine-independent access to the components of a floating-point number.

Minimal complete definition

floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE

Methods

floatRadix :: a -> Integer Source

a constant function, returning the radix of the representation (often 2)

floatDigits :: a -> Int Source

a constant function, returning the number of digits of floatRadix in the significand

floatRange :: a -> (Int, Int) Source

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int) Source

The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat :: Integer -> Int -> a Source

encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

exponent :: a -> Int Source

exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

significand :: a -> a Source

The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

scaleFloat :: Int -> a -> a Source

multiplies a floating-point number by an integer power of the radix

isNaN :: a -> Bool Source

True if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool Source

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool Source

True if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool Source

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool Source

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a Source

a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.

Instances
Instances details
RealFloat CDouble Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

RealFloat CFloat Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

RealFloat Double Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

RealFloat Float Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

RealFloat a => RealFloat (Identity a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

RealFloat a => RealFloat (Down a) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

RealFloat a => RealFloat (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

RealFloat (f (g a)) => RealFloat (Compose f g a) Source

Since: base-4.20.0.0

Instance details

Defined in Data.Functor.Compose

Methods

floatRadix :: Compose f g a -> Integer Source

floatDigits :: Compose f g a -> Int Source

floatRange :: Compose f g a -> (Int, Int) Source

decodeFloat :: Compose f g a -> (Integer, Int) Source

encodeFloat :: Integer -> Int -> Compose f g a Source

exponent :: Compose f g a -> Int Source

significand :: Compose f g a -> Compose f g a Source

scaleFloat :: Int -> Compose f g a -> Compose f g a Source

isNaN :: Compose f g a -> Bool Source

isInfinite :: Compose f g a -> Bool Source

isDenormalized :: Compose f g a -> Bool Source

isNegativeZero :: Compose f g a -> Bool Source

isIEEE :: Compose f g a -> Bool Source

atan2 :: Compose f g a -> Compose f g a -> Compose f g a Source

Numeric functions

subtract :: Num a => a -> a -> a Source

the same as flip (-).

Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.

even :: Integral a => a -> Bool Source

odd :: Integral a => a -> Bool Source

gcd :: Integral a => a -> a -> a Source

gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 4 2 = 2, gcd (-4) 6 = 2, gcd 0 4 = 4. gcd 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types.

lcm :: Integral a => a -> a -> a Source

lcm x y is the smallest positive integer that both x and y divide.

(^) :: (Num a, Integral b) => a -> b -> a infixr 8 Source

raise a number to a non-negative integral power

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 Source

raise a number to an integral power

fromIntegral :: (Integral a, Num b) => a -> b Source

General coercion from Integral types.

WARNING: This function performs silent truncation if the result type is not at least as big as the argument's type.

realToFrac :: (Real a, Fractional b) => a -> b Source

General coercion to Fractional types.

WARNING: This function goes through the Rational type, which does not have values for NaN for example. This means it does not round-trip.

For Double it also behaves differently with or without -O0:

Prelude> realToFrac nan -- With -O0
-Infinity
Prelude> realToFrac nan
NaN

Semigroups and Monoids

class Semigroup a where Source

The class of semigroups (types with an associative binary operation).

Instances should satisfy the following:

Associativity
x <> (y <> z) = (x <> y) <> z

You can alternatively define sconcat instead of (<>), in which case the laws are:

Unit
sconcat (pure x) = x
Multiplication
sconcat (join xss) = sconcat (fmap sconcat xss)

Since: base-4.9.0.0

Minimal complete definition

(<>) | sconcat

Methods

(<>) :: a -> a -> a infixr 6 Source

An associative operation.

Examples
Expand
>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]
>>> Just [1, 2, 3] <> Just [4, 5, 6]
Just [1,2,3,4,5,6]
>>> putStr "Hello, " <> putStrLn "World!"
Hello, World!
Instances
Instances details
Semigroup ByteArray Source

Since: base-4.17.0.0

Instance details

Defined in Data.Array.Byte

Semigroup Void Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: Void -> Void -> Void Source

sconcat :: NonEmpty Void -> Void Source

stimes :: Integral b => b -> Void -> Void Source

Semigroup All Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All Source

sconcat :: NonEmpty All -> All Source

stimes :: Integral b => b -> All -> All Source

Semigroup Any Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any Source

sconcat :: NonEmpty Any -> Any Source

stimes :: Integral b => b -> Any -> Any Source

Semigroup Event Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Semigroup EventLifetime Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Methods

(<>) :: EventLifetime -> EventLifetime -> EventLifetime Source

sconcat :: NonEmpty EventLifetime -> EventLifetime Source

stimes :: Integral b => b -> EventLifetime -> EventLifetime Source

Semigroup Lifetime Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Semigroup ExceptionContext Source
Instance details

Defined in GHC.Internal.Exception.Context

Semigroup Ordering Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Semigroup () Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: () -> () -> () Source

sconcat :: NonEmpty () -> () Source

stimes :: Integral b => b -> () -> () Source

Semigroup (Comparison a) Source

(<>) on comparisons combines results with (<>) @Ordering. Without newtypes this equals liftA2 (liftA2 (<>)).

(<>) :: Comparison a -> Comparison a -> Comparison a
Comparison cmp <> Comparison cmp' = Comparison a a' ->
  cmp a a' <> cmp a a'
Instance details

Defined in Data.Functor.Contravariant

Semigroup (Equivalence a) Source

(<>) on equivalences uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (liftA2 (&&)).

(<>) :: Equivalence a -> Equivalence a -> Equivalence a
Equivalence equiv <> Equivalence equiv' = Equivalence a b ->
  equiv a b && equiv' a b
Instance details

Defined in Data.Functor.Contravariant

Semigroup (Predicate a) Source

(<>) on predicates uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (&&).

(<>) :: Predicate a -> Predicate a -> Predicate a
Predicate pred <> Predicate pred' = Predicate a ->
  pred a && pred' a
Instance details

Defined in Data.Functor.Contravariant

Semigroup (First a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: First a -> First a -> First a Source

sconcat :: NonEmpty (First a) -> First a Source

stimes :: Integral b => b -> First a -> First a Source

Semigroup (Last a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: Last a -> Last a -> Last a Source

sconcat :: NonEmpty (Last a) -> Last a Source

stimes :: Integral b => b -> Last a -> Last a Source

Ord a => Semigroup (Max a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: Max a -> Max a -> Max a Source

sconcat :: NonEmpty (Max a) -> Max a Source

stimes :: Integral b => b -> Max a -> Max a Source

Ord a => Semigroup (Min a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: Min a -> Min a -> Min a Source

sconcat :: NonEmpty (Min a) -> Min a Source

stimes :: Integral b => b -> Min a -> Min a Source

Monoid m => Semigroup (WrappedMonoid m) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Semigroup (NonEmpty a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Semigroup a => Semigroup (STM a) Source

Since: base-4.17.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Methods

(<>) :: STM a -> STM a -> STM a Source

sconcat :: NonEmpty (STM a) -> STM a Source

stimes :: Integral b => b -> STM a -> STM a Source

Bits a => Semigroup (And a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

(<>) :: And a -> And a -> And a Source

sconcat :: NonEmpty (And a) -> And a Source

stimes :: Integral b => b -> And a -> And a Source

FiniteBits a => Semigroup (Iff a) Source

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

(<>) :: Iff a -> Iff a -> Iff a Source

sconcat :: NonEmpty (Iff a) -> Iff a Source

stimes :: Integral b => b -> Iff a -> Iff a Source

Bits a => Semigroup (Ior a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

(<>) :: Ior a -> Ior a -> Ior a Source

sconcat :: NonEmpty (Ior a) -> Ior a Source

stimes :: Integral b => b -> Ior a -> Ior a Source

Bits a => Semigroup (Xor a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

(<>) :: Xor a -> Xor a -> Xor a Source

sconcat :: NonEmpty (Xor a) -> Xor a Source

stimes :: Integral b => b -> Xor a -> Xor a Source

Semigroup a => Semigroup (Identity a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Ord a => Semigroup (Max a) Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

(<>) :: Max a -> Max a -> Max a Source

sconcat :: NonEmpty (Max a) -> Max a Source

stimes :: Integral b => b -> Max a -> Max a Source

Ord a => Semigroup (Min a) Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

(<>) :: Min a -> Min a -> Min a Source

sconcat :: NonEmpty (Min a) -> Min a Source

stimes :: Integral b => b -> Min a -> Min a Source

Semigroup (First a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: First a -> First a -> First a Source

sconcat :: NonEmpty (First a) -> First a Source

stimes :: Integral b => b -> First a -> First a Source

Semigroup (Last a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: Last a -> Last a -> Last a Source

sconcat :: NonEmpty (Last a) -> Last a Source

stimes :: Integral b => b -> Last a -> Last a Source

Semigroup a => Semigroup (Down a) Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

(<>) :: Down a -> Down a -> Down a Source

sconcat :: NonEmpty (Down a) -> Down a Source

stimes :: Integral b => b -> Down a -> Down a Source

Semigroup a => Semigroup (Dual a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Dual a -> Dual a -> Dual a Source

sconcat :: NonEmpty (Dual a) -> Dual a Source

stimes :: Integral b => b -> Dual a -> Dual a Source

Semigroup (Endo a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Endo a -> Endo a -> Endo a Source

sconcat :: NonEmpty (Endo a) -> Endo a Source

stimes :: Integral b => b -> Endo a -> Endo a Source

Num a => Semigroup (Product a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Product a -> Product a -> Product a Source

sconcat :: NonEmpty (Product a) -> Product a Source

stimes :: Integral b => b -> Product a -> Product a Source

Num a => Semigroup (Sum a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Sum a -> Sum a -> Sum a Source

sconcat :: NonEmpty (Sum a) -> Sum a Source

stimes :: Integral b => b -> Sum a -> Sum a Source

(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a) Source

Since: base-4.17.0.0

Instance details

Defined in GHC.Internal.Generics

Semigroup p => Semigroup (Par1 p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(<>) :: Par1 p -> Par1 p -> Par1 p Source

sconcat :: NonEmpty (Par1 p) -> Par1 p Source

stimes :: Integral b => b -> Par1 p -> Par1 p Source

Semigroup a => Semigroup (Q a) Source

Since: ghc-internal-2.17.0.0

Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(<>) :: Q a -> Q a -> Q a Source

sconcat :: NonEmpty (Q a) -> Q a Source

stimes :: Integral b => b -> Q a -> Q a Source

Semigroup a => Semigroup (IO a) Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: IO a -> IO a -> IO a Source

sconcat :: NonEmpty (IO a) -> IO a Source

stimes :: Integral b => b -> IO a -> IO a Source

Semigroup a => Semigroup (Maybe a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a Source

sconcat :: NonEmpty (Maybe a) -> Maybe a Source

stimes :: Integral b => b -> Maybe a -> Maybe a Source

Semigroup a => Semigroup (Solo a) Source

Since: base-4.15

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: Solo a -> Solo a -> Solo a Source

sconcat :: NonEmpty (Solo a) -> Solo a Source

stimes :: Integral b => b -> Solo a -> Solo a Source

Semigroup [a] Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: [a] -> [a] -> [a] Source

sconcat :: NonEmpty [a] -> [a] Source

stimes :: Integral b => b -> [a] -> [a] Source

Semigroup a => Semigroup (Op a b) Source

(<>) @(Op a b) without newtypes is (<>) @(b->a) = liftA2 (<>). This lifts the Semigroup operation (<>) over the output of a.

(<>) :: Op a b -> Op a b -> Op a b
Op f <> Op g = Op a -> f a <> g a
Instance details

Defined in Data.Functor.Contravariant

Methods

(<>) :: Op a b -> Op a b -> Op a b Source

sconcat :: NonEmpty (Op a b) -> Op a b Source

stimes :: Integral b0 => b0 -> Op a b -> Op a b Source

Semigroup (Either a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Either

Methods

(<>) :: Either a b -> Either a b -> Either a b Source

sconcat :: NonEmpty (Either a b) -> Either a b Source

stimes :: Integral b0 => b0 -> Either a b -> Either a b Source

Semigroup (Proxy s) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

(<>) :: Proxy s -> Proxy s -> Proxy s Source

sconcat :: NonEmpty (Proxy s) -> Proxy s Source

stimes :: Integral b => b -> Proxy s -> Proxy s Source

Semigroup (U1 p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(<>) :: U1 p -> U1 p -> U1 p Source

sconcat :: NonEmpty (U1 p) -> U1 p Source

stimes :: Integral b => b -> U1 p -> U1 p Source

Semigroup (V1 p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(<>) :: V1 p -> V1 p -> V1 p Source

sconcat :: NonEmpty (V1 p) -> V1 p Source

stimes :: Integral b => b -> V1 p -> V1 p Source

Semigroup a => Semigroup (ST s a) Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.ST

Methods

(<>) :: ST s a -> ST s a -> ST s a Source

sconcat :: NonEmpty (ST s a) -> ST s a Source

stimes :: Integral b => b -> ST s a -> ST s a Source

(Semigroup a, Semigroup b) => Semigroup (a, b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: (a, b) -> (a, b) -> (a, b) Source

sconcat :: NonEmpty (a, b) -> (a, b) Source

stimes :: Integral b0 => b0 -> (a, b) -> (a, b) Source

Semigroup b => Semigroup (a -> b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: (a -> b) -> (a -> b) -> a -> b Source

sconcat :: NonEmpty (a -> b) -> a -> b Source

stimes :: Integral b0 => b0 -> (a -> b) -> a -> b Source

Semigroup a => Semigroup (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

(<>) :: Const a b -> Const a b -> Const a b Source

sconcat :: NonEmpty (Const a b) -> Const a b Source

stimes :: Integral b0 => b0 -> Const a b -> Const a b Source

(Applicative f, Semigroup a) => Semigroup (Ap f a) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: Ap f a -> Ap f a -> Ap f a Source

sconcat :: NonEmpty (Ap f a) -> Ap f a Source

stimes :: Integral b => b -> Ap f a -> Ap f a Source

Alternative f => Semigroup (Alt f a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Alt f a -> Alt f a -> Alt f a Source

sconcat :: NonEmpty (Alt f a) -> Alt f a Source

stimes :: Integral b => b -> Alt f a -> Alt f a Source

Semigroup (f p) => Semigroup (Rec1 f p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p Source

sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p Source

stimes :: Integral b => b -> Rec1 f p -> Rec1 f p Source

(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source

sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source

stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) Source

(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) Source

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Product

Methods

(<>) :: Product f g a -> Product f g a -> Product f g a Source

sconcat :: NonEmpty (Product f g a) -> Product f g a Source

stimes :: Integral b => b -> Product f g a -> Product f g a Source

(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source

sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p Source

stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p Source

Semigroup c => Semigroup (K1 i c p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(<>) :: K1 i c p -> K1 i c p -> K1 i c p Source

sconcat :: NonEmpty (K1 i c p) -> K1 i c p Source

stimes :: Integral b => b -> K1 i c p -> K1 i c p Source

(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source

sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) Source

stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) Source

Semigroup (f (g a)) => Semigroup (Compose f g a) Source

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Compose

Methods

(<>) :: Compose f g a -> Compose f g a -> Compose f g a Source

sconcat :: NonEmpty (Compose f g a) -> Compose f g a Source

stimes :: Integral b => b -> Compose f g a -> Compose f g a Source

Semigroup (f (g p)) => Semigroup ((f :.: g) p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source

sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p Source

stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p Source

Semigroup (f p) => Semigroup (M1 i c f p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p Source

sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p Source

stimes :: Integral b => b -> M1 i c f p -> M1 i c f p Source

(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source

sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) Source

stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) Source

class Semigroup a => Monoid a where Source

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

Right identity
x <> mempty = x
Left identity
mempty <> x = x
Associativity
x <> (y <> z) = (x <> y) <> z (Semigroup law)
Concatenation
mconcat = foldr (<>) mempty

You can alternatively define mconcat instead of mempty, in which case the laws are:

Unit
mconcat (pure x) = x
Multiplication
mconcat (join xss) = mconcat (fmap mconcat xss)
Subclass
mconcat (toList xs) = sconcat xs

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

Minimal complete definition

mempty | mconcat

Methods

mempty :: a Source

Identity of mappend

Examples
Expand
>>> "Hello world" <> mempty
"Hello world"
>>> mempty <> [1, 2, 3]
[1,2,3]

mappend :: a -> a -> a Source

An associative operation

NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.

mconcat :: [a] -> a Source

Fold a list using the monoid.

For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

>>> mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"
Instances
Instances details
Monoid ByteArray Source

Since: base-4.17.0.0

Instance details

Defined in Data.Array.Byte

Monoid All Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: All Source

mappend :: All -> All -> All Source

mconcat :: [All] -> All Source

Monoid Any Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Any Source

mappend :: Any -> Any -> Any Source

mconcat :: [Any] -> Any Source

Monoid Event Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Monoid EventLifetime Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Methods

mempty :: EventLifetime Source

mappend :: EventLifetime -> EventLifetime -> EventLifetime Source

mconcat :: [EventLifetime] -> EventLifetime Source

Monoid Lifetime Source

mappend takes the longer of two lifetimes.

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Monoid ExceptionContext Source
Instance details

Defined in GHC.Internal.Exception.Context

Monoid Ordering Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Monoid () Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: () Source

mappend :: () -> () -> () Source

mconcat :: [()] -> () Source

Monoid (Comparison a) Source

mempty on comparisons always returns EQ. Without newtypes this equals pure (pure EQ).

mempty :: Comparison a
mempty = Comparison _ _ -> EQ
Instance details

Defined in Data.Functor.Contravariant

Monoid (Equivalence a) Source

mempty on equivalences always returns True. Without newtypes this equals pure (pure True).

mempty :: Equivalence a
mempty = Equivalence _ _ -> True
Instance details

Defined in Data.Functor.Contravariant

Monoid (Predicate a) Source

mempty on predicates always returns True. Without newtypes this equals pure True.

mempty :: Predicate a
mempty = _ -> True
Instance details

Defined in Data.Functor.Contravariant

(Ord a, Bounded a) => Monoid (Max a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Max a Source

mappend :: Max a -> Max a -> Max a Source

mconcat :: [Max a] -> Max a Source

(Ord a, Bounded a) => Monoid (Min a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Min a Source

mappend :: Min a -> Min a -> Min a Source

mconcat :: [Min a] -> Min a Source

Monoid m => Monoid (WrappedMonoid m) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Monoid a => Monoid (STM a) Source

Since: base-4.17.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Methods

mempty :: STM a Source

mappend :: STM a -> STM a -> STM a Source

mconcat :: [STM a] -> STM a Source

FiniteBits a => Monoid (And a) Source

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

mempty :: And a Source

mappend :: And a -> And a -> And a Source

mconcat :: [And a] -> And a Source

FiniteBits a => Monoid (Iff a) Source

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

mempty :: Iff a Source

mappend :: Iff a -> Iff a -> Iff a Source

mconcat :: [Iff a] -> Iff a Source

Bits a => Monoid (Ior a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

mempty :: Ior a Source

mappend :: Ior a -> Ior a -> Ior a Source

mconcat :: [Ior a] -> Ior a Source

Bits a => Monoid (Xor a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

mempty :: Xor a Source

mappend :: Xor a -> Xor a -> Xor a Source

mconcat :: [Xor a] -> Xor a Source

Monoid a => Monoid (Identity a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Ord a => Monoid (Max a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

mempty :: Max a Source

mappend :: Max a -> Max a -> Max a Source

mconcat :: [Max a] -> Max a Source

Ord a => Monoid (Min a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

mempty :: Min a Source

mappend :: Min a -> Min a -> Min a Source

mconcat :: [Min a] -> Min a Source

Monoid (First a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: First a Source

mappend :: First a -> First a -> First a Source

mconcat :: [First a] -> First a Source

Monoid (Last a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Last a Source

mappend :: Last a -> Last a -> Last a Source

mconcat :: [Last a] -> Last a Source

Monoid a => Monoid (Down a) Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

mempty :: Down a Source

mappend :: Down a -> Down a -> Down a Source

mconcat :: [Down a] -> Down a Source

Monoid a => Monoid (Dual a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Dual a Source

mappend :: Dual a -> Dual a -> Dual a Source

mconcat :: [Dual a] -> Dual a Source

Monoid (Endo a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Endo a Source

mappend :: Endo a -> Endo a -> Endo a Source

mconcat :: [Endo a] -> Endo a Source

Num a => Monoid (Product a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Num a => Monoid (Sum a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Sum a Source

mappend :: Sum a -> Sum a -> Sum a Source

mconcat :: [Sum a] -> Sum a Source

(Generic a, Monoid (Rep a ())) => Monoid (Generically a) Source

Since: base-4.17.0.0

Instance details

Defined in GHC.Internal.Generics

Monoid p => Monoid (Par1 p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: Par1 p Source

mappend :: Par1 p -> Par1 p -> Par1 p Source

mconcat :: [Par1 p] -> Par1 p Source

Monoid a => Monoid (Q a) Source

Since: ghc-internal-2.17.0.0

Instance details

Defined in GHC.Internal.TH.Syntax

Methods

mempty :: Q a Source

mappend :: Q a -> Q a -> Q a Source

mconcat :: [Q a] -> Q a Source

Monoid a => Monoid (IO a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: IO a Source

mappend :: IO a -> IO a -> IO a Source

mconcat :: [IO a] -> IO a Source

Semigroup a => Monoid (Maybe a) Source

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S."

Since 4.11.0: constraint on inner a value generalised from Monoid to Semigroup.

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: Maybe a Source

mappend :: Maybe a -> Maybe a -> Maybe a Source

mconcat :: [Maybe a] -> Maybe a Source

Monoid a => Monoid (Solo a) Source

Since: base-4.15

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: Solo a Source

mappend :: Solo a -> Solo a -> Solo a Source

mconcat :: [Solo a] -> Solo a Source

Monoid [a] Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: [a] Source

mappend :: [a] -> [a] -> [a] Source

mconcat :: [[a]] -> [a] Source

Monoid a => Monoid (Op a b) Source

mempty @(Op a b) without newtypes is mempty @(b->a) = _ -> mempty.

mempty :: Op a b
mempty = Op _ -> mempty
Instance details

Defined in Data.Functor.Contravariant

Methods

mempty :: Op a b Source

mappend :: Op a b -> Op a b -> Op a b Source

mconcat :: [Op a b] -> Op a b Source

Monoid (Proxy s) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

mempty :: Proxy s Source

mappend :: Proxy s -> Proxy s -> Proxy s Source

mconcat :: [Proxy s] -> Proxy s Source

Monoid (U1 p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: U1 p Source

mappend :: U1 p -> U1 p -> U1 p Source

mconcat :: [U1 p] -> U1 p Source

Monoid a => Monoid (ST s a) Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.ST

Methods

mempty :: ST s a Source

mappend :: ST s a -> ST s a -> ST s a Source

mconcat :: [ST s a] -> ST s a Source

(Monoid a, Monoid b) => Monoid (a, b) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: (a, b) Source

mappend :: (a, b) -> (a, b) -> (a, b) Source

mconcat :: [(a, b)] -> (a, b) Source

Monoid b => Monoid (a -> b) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: a -> b Source

mappend :: (a -> b) -> (a -> b) -> a -> b Source

mconcat :: [a -> b] -> a -> b Source

Monoid a => Monoid (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

mempty :: Const a b Source

mappend :: Const a b -> Const a b -> Const a b Source

mconcat :: [Const a b] -> Const a b Source

(Applicative f, Monoid a) => Monoid (Ap f a) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Ap f a Source

mappend :: Ap f a -> Ap f a -> Ap f a Source

mconcat :: [Ap f a] -> Ap f a Source

Alternative f => Monoid (Alt f a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Alt f a Source

mappend :: Alt f a -> Alt f a -> Alt f a Source

mconcat :: [Alt f a] -> Alt f a Source

Monoid (f p) => Monoid (Rec1 f p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: Rec1 f p Source

mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p Source

mconcat :: [Rec1 f p] -> Rec1 f p Source

(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: (a, b, c) Source

mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) Source

mconcat :: [(a, b, c)] -> (a, b, c) Source

(Monoid (f a), Monoid (g a)) => Monoid (Product f g a) Source

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Product

Methods

mempty :: Product f g a Source

mappend :: Product f g a -> Product f g a -> Product f g a Source

mconcat :: [Product f g a] -> Product f g a Source

(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: (f :*: g) p Source

mappend :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source

mconcat :: [(f :*: g) p] -> (f :*: g) p Source

Monoid c => Monoid (K1 i c p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: K1 i c p Source

mappend :: K1 i c p -> K1 i c p -> K1 i c p Source

mconcat :: [K1 i c p] -> K1 i c p Source

(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: (a, b, c, d) Source

mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source

mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source

Monoid (f (g a)) => Monoid (Compose f g a) Source

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Compose

Methods

mempty :: Compose f g a Source

mappend :: Compose f g a -> Compose f g a -> Compose f g a Source

mconcat :: [Compose f g a] -> Compose f g a Source

Monoid (f (g p)) => Monoid ((f :.: g) p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: (f :.: g) p Source

mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source

mconcat :: [(f :.: g) p] -> (f :.: g) p Source

Monoid (f p) => Monoid (M1 i c f p) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: M1 i c f p Source

mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p Source

mconcat :: [M1 i c f p] -> M1 i c f p Source

(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: (a, b, c, d, e) Source

mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source

mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source

Monads and functors

class Functor (f :: Type -> Type) where Source

A type f is a Functor if it provides a function fmap which, given any types a and b lets you apply any function from (a -> b) to turn an f a into an f b, preserving the structure of f. Furthermore f needs to adhere to the following:

Identity
fmap id == id
Composition
fmap (f . g) == fmap f . fmap g

Note, that the second law follows from the free theorem of the type fmap and the first law, so you need only check that the former condition holds. See these articles by School of Haskell or David Luposchainsky for an explanation.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b Source

fmap is used to apply a function of type (a -> b) to a value of type f a, where f is a functor, to produce a value of type f b. Note that for any type constructor with more than one parameter (e.g., Either), only the last type parameter can be modified with fmap (e.g., b in `Either a b`).

Some type constructors with two parameters or more have a Bifunctor instance that allows both the last and the penultimate parameters to be mapped over.

Examples
Expand

Convert from a Maybe Int to a Maybe String using show:

>>> fmap show Nothing
Nothing
>>> fmap show (Just 3)
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> fmap show (Left 17)
Left 17
>>> fmap show (Right 17)
Right "17"

Double each element of a list:

>>> fmap (*2) [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> fmap even (2,2)
(2,True)

It may seem surprising that the function is only applied to the last element of the tuple compared to the list example above which applies it to every element in the list. To understand, remember that tuples are type constructors with multiple type parameters: a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over with fmap).

It explains why fmap can be used with tuples containing values of different types as in the following example:

>>> fmap even ("hello", 1.0, 4)
("hello",1.0,True)

(<$) :: a -> f b -> f a infixl 4 Source

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Examples
Expand

Perform a computation with Maybe and replace the result with a constant value if it is Just:

>>> 'a' <$ Just 2
Just 'a'
>>> 'a' <$ Nothing
Nothing
Instances
Instances details
Functor Complex Source

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b Source

(<$) :: a -> Complex b -> Complex a Source

Functor First Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> First a -> First b Source

(<$) :: a -> First b -> First a Source

Functor Last Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Last a -> Last b Source

(<$) :: a -> Last b -> Last a Source

Functor Max Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Max a -> Max b Source

(<$) :: a -> Max b -> Max a Source

Functor Min Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Min a -> Min b Source

(<$) :: a -> Min b -> Min a Source

Functor ArgDescr Source

Since: base-4.7.0.0

Instance details

Defined in System.Console.GetOpt

Methods

fmap :: (a -> b) -> ArgDescr a -> ArgDescr b Source

(<$) :: a -> ArgDescr b -> ArgDescr a Source

Functor ArgOrder Source

Since: base-4.7.0.0

Instance details

Defined in System.Console.GetOpt

Methods

fmap :: (a -> b) -> ArgOrder a -> ArgOrder b Source

(<$) :: a -> ArgOrder b -> ArgOrder a Source

Functor OptDescr Source

Since: base-4.7.0.0

Instance details

Defined in System.Console.GetOpt

Methods

fmap :: (a -> b) -> OptDescr a -> OptDescr b Source

(<$) :: a -> OptDescr b -> OptDescr a Source

Functor NonEmpty Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source

(<$) :: a -> NonEmpty b -> NonEmpty a Source

Functor STM Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Methods

fmap :: (a -> b) -> STM a -> STM b Source

(<$) :: a -> STM b -> STM a Source

Functor Handler Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Control.Exception

Methods

fmap :: (a -> b) -> Handler a -> Handler b Source

(<$) :: a -> Handler b -> Handler a Source

Functor Identity Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Methods

fmap :: (a -> b) -> Identity a -> Identity b Source

(<$) :: a -> Identity b -> Identity a Source

Functor First Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

fmap :: (a -> b) -> First a -> First b Source

(<$) :: a -> First b -> First a Source

Functor Last Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

fmap :: (a -> b) -> Last a -> Last b Source

(<$) :: a -> Last b -> Last a Source

Functor Down Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

fmap :: (a -> b) -> Down a -> Down b Source

(<$) :: a -> Down b -> Down a Source

Functor Dual Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Dual a -> Dual b Source

(<$) :: a -> Dual b -> Dual a Source

Functor Product Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Product a -> Product b Source

(<$) :: a -> Product b -> Product a Source

Functor Sum Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Sum a -> Sum b Source

(<$) :: a -> Sum b -> Sum a Source

Functor ZipList Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

fmap :: (a -> b) -> ZipList a -> ZipList b Source

(<$) :: a -> ZipList b -> ZipList a Source

Functor NoIO Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.GHCi

Methods

fmap :: (a -> b) -> NoIO a -> NoIO b Source

(<$) :: a -> NoIO b -> NoIO a Source

Functor Par1 Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> Par1 a -> Par1 b Source

(<$) :: a -> Par1 b -> Par1 a Source

Functor Q Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

fmap :: (a -> b) -> Q a -> Q b Source

(<$) :: a -> Q b -> Q a Source

Functor TyVarBndr Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

fmap :: (a -> b) -> TyVarBndr a -> TyVarBndr b Source

(<$) :: a -> TyVarBndr b -> TyVarBndr a Source

Functor P Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadP

Methods

fmap :: (a -> b) -> P a -> P b Source

(<$) :: a -> P b -> P a Source

Functor ReadP Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadP

Methods

fmap :: (a -> b) -> ReadP a -> ReadP b Source

(<$) :: a -> ReadP b -> ReadP a Source

Functor ReadPrec Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadPrec

Methods

fmap :: (a -> b) -> ReadPrec a -> ReadPrec b Source

(<$) :: a -> ReadPrec b -> ReadPrec a Source

Functor IO Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a -> b) -> IO a -> IO b Source

(<$) :: a -> IO b -> IO a Source

Functor Maybe Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b Source

(<$) :: a -> Maybe b -> Maybe a Source

Functor Solo Source

Since: base-4.15

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a -> b) -> Solo a -> Solo b Source

(<$) :: a -> Solo b -> Solo a Source

Functor [] Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a -> b) -> [a] -> [b] Source

(<$) :: a -> [b] -> [a] Source

Monad m => Functor (WrappedMonad m) Source

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source

(<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source

Functor (Arg a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source

(<$) :: a0 -> Arg a b -> Arg a a0 Source

Functor (Array i) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Arr

Methods

fmap :: (a -> b) -> Array i a -> Array i b Source

(<$) :: a -> Array i b -> Array i a Source

Arrow a => Functor (ArrowMonad a) Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source

(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source

Functor (ST s) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Control.Monad.ST.Lazy.Imp

Methods

fmap :: (a -> b) -> ST s a -> ST s b Source

(<$) :: a -> ST s b -> ST s a Source

Functor (Either a) Source

Since: base-3.0

Instance details

Defined in GHC.Internal.Data.Either

Methods

fmap :: (a0 -> b) -> Either a a0 -> Either a b Source

(<$) :: a0 -> Either a b -> Either a a0 Source

Functor (StateL s) Source

Since: base-4.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

fmap :: (a -> b) -> StateL s a -> StateL s b Source

(<$) :: a -> StateL s b -> StateL s a Source

Functor (StateR s) Source

Since: base-4.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

fmap :: (a -> b) -> StateR s a -> StateR s b Source

(<$) :: a -> StateR s b -> StateR s a Source

Functor (Proxy :: Type -> Type) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

fmap :: (a -> b) -> Proxy a -> Proxy b Source

(<$) :: a -> Proxy b -> Proxy a Source

Functor (U1 :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> U1 a -> U1 b Source

(<$) :: a -> U1 b -> U1 a Source

Functor (V1 :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> V1 a -> V1 b Source

(<$) :: a -> V1 b -> V1 a Source

Functor (ST s) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.ST

Methods

fmap :: (a -> b) -> ST s a -> ST s b Source

(<$) :: a -> ST s b -> ST s a Source

Functor ((,) a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a0 -> b) -> (a, a0) -> (a, b) Source

(<$) :: a0 -> (a, b) -> (a, a0) Source

Arrow a => Functor (WrappedArrow a b) Source

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source

(<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source

Functor m => Functor (Kleisli m a) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

fmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source

(<$) :: a0 -> Kleisli m a b -> Kleisli m a a0 Source

Functor (Const m :: Type -> Type) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

fmap :: (a -> b) -> Const m a -> Const m b Source

(<$) :: a -> Const m b -> Const m a Source

Monad m => Functor (StateT s m) Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

fmap :: (a -> b) -> StateT s m a -> StateT s m b Source

(<$) :: a -> StateT s m b -> StateT s m a Source

Functor f => Functor (Ap f) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

fmap :: (a -> b) -> Ap f a -> Ap f b Source

(<$) :: a -> Ap f b -> Ap f a Source

Functor f => Functor (Alt f) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Alt f a -> Alt f b Source

(<$) :: a -> Alt f b -> Alt f a Source

(Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) Source

Since: base-4.17.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source

(<$) :: a -> Generically1 f b -> Generically1 f a Source

Functor f => Functor (Rec1 f) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> Rec1 f a -> Rec1 f b Source

(<$) :: a -> Rec1 f b -> Rec1 f a Source

Functor (URec (Ptr ()) :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b Source

(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a Source

Functor (URec Char :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Char a -> URec Char b Source

(<$) :: a -> URec Char b -> URec Char a Source

Functor (URec Double :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b Source

(<$) :: a -> URec Double b -> URec Double a Source

Functor (URec Float :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Float a -> URec Float b Source

(<$) :: a -> URec Float b -> URec Float a Source

Functor (URec Int :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Int a -> URec Int b Source

(<$) :: a -> URec Int b -> URec Int a Source

Functor (URec Word :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Word a -> URec Word b Source

(<$) :: a -> URec Word b -> URec Word a Source

Functor ((,,) a b) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source

(<$) :: a0 -> (a, b, b0) -> (a, b, a0) Source

(Functor f, Functor g) => Functor (Product f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

fmap :: (a -> b) -> Product f g a -> Product f g b Source

(<$) :: a -> Product f g b -> Product f g a Source

(Functor f, Functor g) => Functor (Sum f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

Methods

fmap :: (a -> b) -> Sum f g a -> Sum f g b Source

(<$) :: a -> Sum f g b -> Sum f g a Source

(Functor f, Functor g) => Functor (f :*: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b Source

(<$) :: a -> (f :*: g) b -> (f :*: g) a Source

(Functor f, Functor g) => Functor (f :+: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b Source

(<$) :: a -> (f :+: g) b -> (f :+: g) a Source

Functor (K1 i c :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> K1 i c a -> K1 i c b Source

(<$) :: a -> K1 i c b -> K1 i c a Source

Functor ((,,,) a b c) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source

(<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0) Source

Functor ((->) r) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a -> b) -> (r -> a) -> r -> b Source

(<$) :: a -> (r -> b) -> r -> a Source

(Functor f, Functor g) => Functor (Compose f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

fmap :: (a -> b) -> Compose f g a -> Compose f g b Source

(<$) :: a -> Compose f g b -> Compose f g a Source

(Functor f, Functor g) => Functor (f :.: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b Source

(<$) :: a -> (f :.: g) b -> (f :.: g) a Source

Functor f => Functor (M1 i c f) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> M1 i c f a -> M1 i c f b Source

(<$) :: a -> M1 i c f b -> M1 i c f a Source

Functor ((,,,,) a b c d) Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a0 -> b0) -> (a, b, c, d, a0) -> (a, b, c, d, b0) Source

(<$) :: a0 -> (a, b, c, d, b0) -> (a, b, c, d, a0) Source

Functor ((,,,,,) a b c d e) Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a0 -> b0) -> (a, b, c, d, e, a0) -> (a, b, c, d, e, b0) Source

(<$) :: a0 -> (a, b, c, d, e, b0) -> (a, b, c, d, e, a0) Source

Functor ((,,,,,,) a b c d e f) Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a0 -> b0) -> (a, b, c, d, e, f, a0) -> (a, b, c, d, e, f, b0) Source

(<$) :: a0 -> (a, b, c, d, e, f, b0) -> (a, b, c, d, e, f, a0) Source

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source

An infix synonym for fmap.

The name of this operator is an allusion to $. Note the similarities between their types:

 ($)  ::              (a -> b) ->   a ->   b
(<$>) :: Functor f => (a -> b) -> f a -> f b

Whereas $ is function application, <$> is function application lifted over a Functor.

Examples
Expand

Convert from a Maybe Int to a Maybe String using show:

>>> show <$> Nothing
Nothing
>>> show <$> Just 3
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> show <$> Left 17
Left 17
>>> show <$> Right 17
Right "17"

Double each element of a list:

>>> (*2) <$> [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> even <$> (2,2)
(2,True)

class Functor f => Applicative (f :: Type -> Type) where Source

A functor with application, providing operations to

A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:

(<*>) = liftA2 id
liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

Identity
pure id <*> v = v
Composition
pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
Homomorphism
pure f <*> pure x = pure (f x)
Interchange
u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

As a consequence of these laws, the Functor instance for f will satisfy

It may be useful to note that supposing

forall x y. p (q x y) = f x . g y

it follows from the above that

liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v

If f is also a Monad, it should satisfy

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a Source

Lift a value into the Structure.

Examples
Expand
>>> pure 1 :: Maybe Int
Just 1
>>> pure 'z' :: [Char]
"z"
>>> pure (pure ":D") :: Maybe [String]
Just [":D"]

(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source

Sequential application.

A few functors support an implementation of <*> that is more efficient than the default one.

Example
Expand

Used in combination with (<$>), (<*>) can be used to build a record.

>>> data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
>>> produceFoo :: Applicative f => f Foo
>>> produceBar :: Applicative f => f Bar
>>> produceBaz :: Applicative f => f Baz
>>> mkState :: Applicative f => f MyState
>>> mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz

liftA2 :: (a -> b -> c) -> f a -> f b -> f c Source

Lift a binary function to actions.

Some functors support an implementation of liftA2 that is more efficient than the default one. In particular, if fmap is an expensive operation, it is likely better to use liftA2 than to fmap over the structure and then use <*>.

This became a typeclass method in 4.10.0.0. Prior to that, it was a function defined in terms of <*> and fmap.

Example
Expand
>>> liftA2 (,) (Just 3) (Just 5)
Just (3,5)
>>> liftA2 (+) [1, 2, 3] [4, 5, 6]
[5,6,7,6,7,8,7,8,9]

(*>) :: f a -> f b -> f b infixl 4 Source

Sequence actions, discarding the value of the first argument.

Examples
Expand

If used in conjunction with the Applicative instance for Maybe, you can chain Maybe computations, with a possible "early return" in case of Nothing.

>>> Just 2 *> Just 3
Just 3
>>> Nothing *> Just 3
Nothing

Of course a more interesting use case would be to have effectful computations instead of just returning pure values.

>>> import Data.Char
>>> import GHC.Internal.Text.ParserCombinators.ReadP
>>> let p = string "my name is " *> munch1 isAlpha <* eof
>>> readP_to_S p "my name is Simon"
[("Simon","")]

(<*) :: f a -> f b -> f a infixl 4 Source

Sequence actions, discarding the value of the second argument.

Instances
Instances details
Applicative Complex Source

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Methods

pure :: a -> Complex a Source

(<*>) :: Complex (a -> b) -> Complex a -> Complex b Source

liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c Source

(*>) :: Complex a -> Complex b -> Complex b Source

(<*) :: Complex a -> Complex b -> Complex a Source

Applicative First Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> First a Source

(<*>) :: First (a -> b) -> First a -> First b Source

liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source

(*>) :: First a -> First b -> First b Source

(<*) :: First a -> First b -> First a Source

Applicative Last Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Last a Source

(<*>) :: Last (a -> b) -> Last a -> Last b Source

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source

(*>) :: Last a -> Last b -> Last b Source

(<*) :: Last a -> Last b -> Last a Source

Applicative Max Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Max a Source

(<*>) :: Max (a -> b) -> Max a -> Max b Source

liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source

(*>) :: Max a -> Max b -> Max b Source

(<*) :: Max a -> Max b -> Max a Source

Applicative Min Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Min a Source

(<*>) :: Min (a -> b) -> Min a -> Min b Source

liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source

(*>) :: Min a -> Min b -> Min b Source

(<*) :: Min a -> Min b -> Min a Source

Applicative NonEmpty Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> NonEmpty a Source

(<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source

liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source

(*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source

(<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source

Applicative STM Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Methods

pure :: a -> STM a Source

(<*>) :: STM (a -> b) -> STM a -> STM b Source

liftA2 :: (a -> b -> c) -> STM a -> STM b -> STM c Source

(*>) :: STM a -> STM b -> STM b Source

(<*) :: STM a -> STM b -> STM a Source

Applicative Identity Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Methods

pure :: a -> Identity a Source

(<*>) :: Identity (a -> b) -> Identity a -> Identity b Source

liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c Source

(*>) :: Identity a -> Identity b -> Identity b Source

(<*) :: Identity a -> Identity b -> Identity a Source

Applicative First Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> First a Source

(<*>) :: First (a -> b) -> First a -> First b Source

liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source

(*>) :: First a -> First b -> First b Source

(<*) :: First a -> First b -> First a Source

Applicative Last Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> Last a Source

(<*>) :: Last (a -> b) -> Last a -> Last b Source

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source

(*>) :: Last a -> Last b -> Last b Source

(<*) :: Last a -> Last b -> Last a Source

Applicative Down Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

pure :: a -> Down a Source

(<*>) :: Down (a -> b) -> Down a -> Down b Source

liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c Source

(*>) :: Down a -> Down b -> Down b Source

(<*) :: Down a -> Down b -> Down a Source

Applicative Dual Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Dual a Source

(<*>) :: Dual (a -> b) -> Dual a -> Dual b Source

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source

(*>) :: Dual a -> Dual b -> Dual b Source

(<*) :: Dual a -> Dual b -> Dual a Source

Applicative Product Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Product a Source

(<*>) :: Product (a -> b) -> Product a -> Product b Source

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source

(*>) :: Product a -> Product b -> Product b Source

(<*) :: Product a -> Product b -> Product a Source

Applicative Sum Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Sum a Source

(<*>) :: Sum (a -> b) -> Sum a -> Sum b Source

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source

(*>) :: Sum a -> Sum b -> Sum b Source

(<*) :: Sum a -> Sum b -> Sum a Source

Applicative ZipList Source
f <$> ZipList xs1 <*> ... <*> ZipList xsN
    = ZipList (zipWithN f xs1 ... xsN)

where zipWithN refers to the zipWith function of the appropriate arity (zipWith, zipWith3, zipWith4, ...). For example:

(\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
    = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
    = ZipList {getZipList = ["a5","b6b6","c7c7c7"]}

Since: base-2.1

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

pure :: a -> ZipList a Source

(<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source

liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c Source

(*>) :: ZipList a -> ZipList b -> ZipList b Source

(<*) :: ZipList a -> ZipList b -> ZipList a Source

Applicative NoIO Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.GHCi

Methods

pure :: a -> NoIO a Source

(<*>) :: NoIO (a -> b) -> NoIO a -> NoIO b Source

liftA2 :: (a -> b -> c) -> NoIO a -> NoIO b -> NoIO c Source

(*>) :: NoIO a -> NoIO b -> NoIO b Source

(<*) :: NoIO a -> NoIO b -> NoIO a Source

Applicative Par1 Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> Par1 a Source

(<*>) :: Par1 (a -> b) -> Par1 a -> Par1 b Source

liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c Source

(*>) :: Par1 a -> Par1 b -> Par1 b Source

(<*) :: Par1 a -> Par1 b -> Par1 a Source

Applicative Q Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

pure :: a -> Q a Source

(<*>) :: Q (a -> b) -> Q a -> Q b Source

liftA2 :: (a -> b -> c) -> Q a -> Q b -> Q c Source

(*>) :: Q a -> Q b -> Q b Source

(<*) :: Q a -> Q b -> Q a Source

Applicative P Source

Since: base-4.5.0.0

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadP

Methods

pure :: a -> P a Source

(<*>) :: P (a -> b) -> P a -> P b Source

liftA2 :: (a -> b -> c) -> P a -> P b -> P c Source

(*>) :: P a -> P b -> P b Source

(<*) :: P a -> P b -> P a Source

Applicative ReadP Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadP

Methods

pure :: a -> ReadP a Source

(<*>) :: ReadP (a -> b) -> ReadP a -> ReadP b Source

liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c Source

(*>) :: ReadP a -> ReadP b -> ReadP b Source

(<*) :: ReadP a -> ReadP b -> ReadP a Source

Applicative ReadPrec Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadPrec

Methods

pure :: a -> ReadPrec a Source

(<*>) :: ReadPrec (a -> b) -> ReadPrec a -> ReadPrec b Source

liftA2 :: (a -> b -> c) -> ReadPrec a -> ReadPrec b -> ReadPrec c Source

(*>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source

(<*) :: ReadPrec a -> ReadPrec b -> ReadPrec a Source

Applicative IO Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> IO a Source

(<*>) :: IO (a -> b) -> IO a -> IO b Source

liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source

(*>) :: IO a -> IO b -> IO b Source

(<*) :: IO a -> IO b -> IO a Source

Applicative Maybe Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> Maybe a Source

(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source

liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source

(*>) :: Maybe a -> Maybe b -> Maybe b Source

(<*) :: Maybe a -> Maybe b -> Maybe a Source

Applicative Solo Source

Since: base-4.15

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> Solo a Source

(<*>) :: Solo (a -> b) -> Solo a -> Solo b Source

liftA2 :: (a -> b -> c) -> Solo a -> Solo b -> Solo c Source

(*>) :: Solo a -> Solo b -> Solo b Source

(<*) :: Solo a -> Solo b -> Solo a Source

Applicative [] Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> [a] Source

(<*>) :: [a -> b] -> [a] -> [b] Source

liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] Source

(*>) :: [a] -> [b] -> [b] Source

(<*) :: [a] -> [b] -> [a] Source

Monad m => Applicative (WrappedMonad m) Source

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

pure :: a -> WrappedMonad m a Source

(<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source

liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source

(*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source

(<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source

Arrow a => Applicative (ArrowMonad a) Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

pure :: a0 -> ArrowMonad a a0 Source

(<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source

liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source

(*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source

(<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source

Applicative (ST s) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Control.Monad.ST.Lazy.Imp

Methods

pure :: a -> ST s a Source

(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source

liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source

(*>) :: ST s a -> ST s b -> ST s b Source

(<*) :: ST s a -> ST s b -> ST s a Source

Applicative (Either e) Source

Since: base-3.0

Instance details

Defined in GHC.Internal.Data.Either

Methods

pure :: a -> Either e a Source

(<*>) :: Either e (a -> b) -> Either e a -> Either e b Source

liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source

(*>) :: Either e a -> Either e b -> Either e b Source

(<*) :: Either e a -> Either e b -> Either e a Source

Applicative (StateL s) Source

Since: base-4.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

pure :: a -> StateL s a Source

(<*>) :: StateL s (a -> b) -> StateL s a -> StateL s b Source

liftA2 :: (a -> b -> c) -> StateL s a -> StateL s b -> StateL s c Source

(*>) :: StateL s a -> StateL s b -> StateL s b Source

(<*) :: StateL s a -> StateL s b -> StateL s a Source

Applicative (StateR s) Source

Since: base-4.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

pure :: a -> StateR s a Source

(<*>) :: StateR s (a -> b) -> StateR s a -> StateR s b Source

liftA2 :: (a -> b -> c) -> StateR s a -> StateR s b -> StateR s c Source

(*>) :: StateR s a -> StateR s b -> StateR s b Source

(<*) :: StateR s a -> StateR s b -> StateR s a Source

Applicative (Proxy :: Type -> Type) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

pure :: a -> Proxy a Source

(<*>) :: Proxy (a -> b) -> Proxy a -> Proxy b Source

liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c Source

(*>) :: Proxy a -> Proxy b -> Proxy b Source

(<*) :: Proxy a -> Proxy b -> Proxy a Source

Applicative (U1 :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> U1 a Source

(<*>) :: U1 (a -> b) -> U1 a -> U1 b Source

liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c Source

(*>) :: U1 a -> U1 b -> U1 b Source

(<*) :: U1 a -> U1 b -> U1 a Source

Applicative (ST s) Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.ST

Methods

pure :: a -> ST s a Source

(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source

liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source

(*>) :: ST s a -> ST s b -> ST s b Source

(<*) :: ST s a -> ST s b -> ST s a Source

Monoid a => Applicative ((,) a) Source

For tuples, the Monoid constraint on a determines how the first values merge. For example, Strings concatenate:

("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a0 -> (a, a0) Source

(<*>) :: (a, a0 -> b) -> (a, a0) -> (a, b) Source

liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c) Source

(*>) :: (a, a0) -> (a, b) -> (a, b) Source

(<*) :: (a, a0) -> (a, b) -> (a, a0) Source

Arrow a => Applicative (WrappedArrow a b) Source

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

pure :: a0 -> WrappedArrow a b a0 Source

(<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source

liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source

(*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source

(<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source

Applicative m => Applicative (Kleisli m a) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

pure :: a0 -> Kleisli m a a0 Source

(<*>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source

liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source

(*>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source

(<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source

Monoid m => Applicative (Const m :: Type -> Type) Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

pure :: a -> Const m a Source

(<*>) :: Const m (a -> b) -> Const m a -> Const m b Source

liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source

(*>) :: Const m a -> Const m b -> Const m b Source

(<*) :: Const m a -> Const m b -> Const m a Source

Monad m => Applicative (StateT s m) Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

pure :: a -> StateT s m a Source

(<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source

liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source

(*>) :: StateT s m a -> StateT s m b -> StateT s m b Source

(<*) :: StateT s m a -> StateT s m b -> StateT s m a Source

Applicative f => Applicative (Ap f) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> Ap f a Source

(<*>) :: Ap f (a -> b) -> Ap f a -> Ap f b Source

liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c Source

(*>) :: Ap f a -> Ap f b -> Ap f b Source

(<*) :: Ap f a -> Ap f b -> Ap f a Source

Applicative f => Applicative (Alt f) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Alt f a Source

(<*>) :: Alt f (a -> b) -> Alt f a -> Alt f b Source

liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source

(*>) :: Alt f a -> Alt f b -> Alt f b Source

(<*) :: Alt f a -> Alt f b -> Alt f a Source

(Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f) Source

Since: base-4.17.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> Generically1 f a Source

(<*>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b Source

liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c Source

(*>) :: Generically1 f a -> Generically1 f b -> Generically1 f b Source

(<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a Source

Applicative f => Applicative (Rec1 f) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> Rec1 f a Source

(<*>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b Source

liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c Source

(*>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source

(<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a Source

(Monoid a, Monoid b) => Applicative ((,,) a b) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a0 -> (a, b, a0) Source

(<*>) :: (a, b, a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source

liftA2 :: (a0 -> b0 -> c) -> (a, b, a0) -> (a, b, b0) -> (a, b, c) Source

(*>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source

(<*) :: (a, b, a0) -> (a, b, b0) -> (a, b, a0) Source

(Applicative f, Applicative g) => Applicative (Product f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

pure :: a -> Product f g a Source

(<*>) :: Product f g (a -> b) -> Product f g a -> Product f g b Source

liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c Source

(*>) :: Product f g a -> Product f g b -> Product f g b Source

(<*) :: Product f g a -> Product f g b -> Product f g a Source

(Applicative f, Applicative g) => Applicative (f :*: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> (f :*: g) a Source

(<*>) :: (f :*: g) (a -> b) -> (f :*: g) a -> (f :*: g) b Source

liftA2 :: (a -> b -> c) -> (f :*: g) a -> (f :*: g) b -> (f :*: g) c Source

(*>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b Source

(<*) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) a Source

Monoid c => Applicative (K1 i c :: Type -> Type) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> K1 i c a Source

(<*>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b Source

liftA2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0 Source

(*>) :: K1 i c a -> K1 i c b -> K1 i c b Source

(<*) :: K1 i c a -> K1 i c b -> K1 i c a Source

(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a0 -> (a, b, c, a0) Source

(<*>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source

liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) Source

(*>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source

(<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) Source

Applicative ((->) r) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> r -> a Source

(<*>) :: (r -> (a -> b)) -> (r -> a) -> r -> b Source

liftA2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> r -> c Source

(*>) :: (r -> a) -> (r -> b) -> r -> b Source

(<*) :: (r -> a) -> (r -> b) -> r -> a Source

(Applicative f, Applicative g) => Applicative (Compose f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

pure :: a -> Compose f g a Source

(<*>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source

liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source

(*>) :: Compose f g a -> Compose f g b -> Compose f g b Source

(<*) :: Compose f g a -> Compose f g b -> Compose f g a Source

(Applicative f, Applicative g) => Applicative (f :.: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> (f :.: g) a Source

(<*>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b Source

liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c Source

(*>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b Source

(<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a Source

Applicative f => Applicative (M1 i c f) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> M1 i c f a Source

(<*>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b Source

liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 Source

(*>) :: M1 i c f a -> M1 i c f b -> M1 i c f b Source

(<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a Source

class Applicative m => Monad (m :: Type -> Type) where Source

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following:

Left identity
return a >>= k = k a
Right identity
m >>= return = m
Associativity
m >>= (\x -> k x >>= h) = (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

The above laws imply:

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for List, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1 Source

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

'as >>= bs' can be understood as the do expression

do a <- as
   bs a

An alternative name for this function is 'bind', but some people may refer to it as 'flatMap', which results from it being equivalent to

\x f -> join (fmap f x) :: Monad m => m a -> (a -> m b) -> m b

which can be seen as mapping a value with Monad m => m a -> m (m b) and then 'flattening' m (m b) to m b using join.

(>>) :: m a -> m b -> m b infixl 1 Source

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

'as >> bs' can be understood as the do expression

do as
   bs

or in terms of (>>=) as

as >>= const bs

return :: a -> m a Source

Inject a value into the monadic type. This function should not be different from its default implementation as pure. The justification for the existence of this function is merely historic.

Instances
Instances details
Monad Complex Source

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Methods

(>>=) :: Complex a -> (a -> Complex b) -> Complex b Source

(>>) :: Complex a -> Complex b -> Complex b Source

return :: a -> Complex a Source

Monad First Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: First a -> (a -> First b) -> First b Source

(>>) :: First a -> First b -> First b Source

return :: a -> First a Source

Monad Last Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b Source

(>>) :: Last a -> Last b -> Last b Source

return :: a -> Last a Source

Monad Max Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: Max a -> (a -> Max b) -> Max b Source

(>>) :: Max a -> Max b -> Max b Source

return :: a -> Max a Source

Monad Min Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: Min a -> (a -> Min b) -> Min b Source

(>>) :: Min a -> Min b -> Min b Source

return :: a -> Min a Source

Monad NonEmpty Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source

(>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source

return :: a -> NonEmpty a Source

Monad STM Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Methods

(>>=) :: STM a -> (a -> STM b) -> STM b Source

(>>) :: STM a -> STM b -> STM b Source

return :: a -> STM a Source

Monad Identity Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Methods

(>>=) :: Identity a -> (a -> Identity b) -> Identity b Source

(>>) :: Identity a -> Identity b -> Identity b Source

return :: a -> Identity a Source

Monad First Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(>>=) :: First a -> (a -> First b) -> First b Source

(>>) :: First a -> First b -> First b Source

return :: a -> First a Source

Monad Last Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b Source

(>>) :: Last a -> Last b -> Last b Source

return :: a -> Last a Source

Monad Down Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

(>>=) :: Down a -> (a -> Down b) -> Down b Source

(>>) :: Down a -> Down b -> Down b Source

return :: a -> Down a Source

Monad Dual Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(>>=) :: Dual a -> (a -> Dual b) -> Dual b Source

(>>) :: Dual a -> Dual b -> Dual b Source

return :: a -> Dual a Source

Monad Product Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b Source

(>>) :: Product a -> Product b -> Product b Source

return :: a -> Product a Source

Monad Sum Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b Source

(>>) :: Sum a -> Sum b -> Sum b Source

return :: a -> Sum a Source

Monad NoIO Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.GHCi

Methods

(>>=) :: NoIO a -> (a -> NoIO b) -> NoIO b Source

(>>) :: NoIO a -> NoIO b -> NoIO b Source

return :: a -> NoIO a Source

Monad Par1 Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b Source

(>>) :: Par1 a -> Par1 b -> Par1 b Source

return :: a -> Par1 a Source

Monad Q Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

(>>=) :: Q a -> (a -> Q b) -> Q b Source

(>>) :: Q a -> Q b -> Q b Source

return :: a -> Q a Source

Monad P Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadP

Methods

(>>=) :: P a -> (a -> P b) -> P b Source

(>>) :: P a -> P b -> P b Source

return :: a -> P a Source

Monad ReadP Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadP

Methods

(>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b Source

(>>) :: ReadP a -> ReadP b -> ReadP b Source

return :: a -> ReadP a Source

Monad ReadPrec Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadPrec

Methods

(>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b Source

(>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source

return :: a -> ReadPrec a Source

Monad IO Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b Source

(>>) :: IO a -> IO b -> IO b Source

return :: a -> IO a Source

Monad Maybe Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source

(>>) :: Maybe a -> Maybe b -> Maybe b Source

return :: a -> Maybe a Source

Monad Solo Source

Since: base-4.15

Instance details

Defined in GHC.Internal.Base

Methods

(>>=) :: Solo a -> (a -> Solo b) -> Solo b Source

(>>) :: Solo a -> Solo b -> Solo b Source

return :: a -> Solo a Source

Monad [] Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

(>>=) :: [a] -> (a -> [b]) -> [b] Source

(>>) :: [a] -> [b] -> [b] Source

return :: a -> [a] Source

Monad m => Monad (WrappedMonad m) Source

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

(>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source

(>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source

return :: a -> WrappedMonad m a Source

ArrowApply a => Monad (ArrowMonad a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

(>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b Source

(>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source

return :: a0 -> ArrowMonad a a0 Source

Monad (ST s) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Control.Monad.ST.Lazy.Imp

Methods

(>>=) :: ST s a -> (a -> ST s b) -> ST s b Source

(>>) :: ST s a -> ST s b -> ST s b Source

return :: a -> ST s a Source

Monad (Either e) Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Data.Either

Methods

(>>=) :: Either e a -> (a -> Either e b) -> Either e b Source

(>>) :: Either e a -> Either e b -> Either e b Source

return :: a -> Either e a Source

Monad (Proxy :: Type -> Type) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

(>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b Source

(>>) :: Proxy a -> Proxy b -> Proxy b Source

return :: a -> Proxy a Source

Monad (U1 :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(>>=) :: U1 a -> (a -> U1 b) -> U1 b Source

(>>) :: U1 a -> U1 b -> U1 b Source

return :: a -> U1 a Source

Monad (ST s) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.ST

Methods

(>>=) :: ST s a -> (a -> ST s b) -> ST s b Source

(>>) :: ST s a -> ST s b -> ST s b Source

return :: a -> ST s a Source

Monoid a => Monad ((,) a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) Source

(>>) :: (a, a0) -> (a, b) -> (a, b) Source

return :: a0 -> (a, a0) Source

Monad m => Monad (Kleisli m a) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

(>>=) :: Kleisli m a a0 -> (a0 -> Kleisli m a b) -> Kleisli m a b Source

(>>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source

return :: a0 -> Kleisli m a a0 Source

Monad m => Monad (StateT s m) Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

(>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b Source

(>>) :: StateT s m a -> StateT s m b -> StateT s m b Source

return :: a -> StateT s m a Source

Monad f => Monad (Ap f) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b Source

(>>) :: Ap f a -> Ap f b -> Ap f b Source

return :: a -> Ap f a Source

Monad f => Monad (Alt f) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b Source

(>>) :: Alt f a -> Alt f b -> Alt f b Source

return :: a -> Alt f a Source

Monad f => Monad (Rec1 f) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b Source

(>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source

return :: a -> Rec1 f a Source

(Monoid a, Monoid b) => Monad ((,,) a b) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(>>=) :: (a, b, a0) -> (a0 -> (a, b, b0)) -> (a, b, b0) Source

(>>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source

return :: a0 -> (a, b, a0) Source

(Monad f, Monad g) => Monad (Product f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

(>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b Source

(>>) :: Product f g a -> Product f g b -> Product f g b Source

return :: a -> Product f g a Source

(Monad f, Monad g) => Monad (f :*: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(>>=) :: (f :*: g) a -> (a -> (f :*: g) b) -> (f :*: g) b Source

(>>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b Source

return :: a -> (f :*: g) a Source

(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(>>=) :: (a, b, c, a0) -> (a0 -> (a, b, c, b0)) -> (a, b, c, b0) Source

(>>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source

return :: a0 -> (a, b, c, a0) Source

Monad ((->) r) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

(>>=) :: (r -> a) -> (a -> r -> b) -> r -> b Source

(>>) :: (r -> a) -> (r -> b) -> r -> b Source

return :: a -> r -> a Source

Monad f => Monad (M1 i c f) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b Source

(>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b Source

return :: a -> M1 i c f a Source

class Monad m => MonadFail (m :: Type -> Type) where Source

When a value is bound in do-notation, the pattern on the left hand side of <- might not match. In this case, this class provides a function to recover.

A Monad without a MonadFail instance may only be used in conjunction with pattern that always match, such as newtypes, tuples, data types with only a single data constructor, and irrefutable patterns (~pat).

Instances of MonadFail should satisfy the following law: fail s should be a left zero for >>=,

fail s >>= f  =  fail s

If your Monad is also MonadPlus, a popular definition is

fail _ = mzero

fail s should be an action that runs in the monad itself, not an exception (except in instances of MonadIO). In particular, fail should not be implemented in terms of error.

Since: base-4.9.0.0

Methods

fail :: String -> m a Source

Instances
Instances details
MonadFail Q Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

fail :: String -> Q a Source

MonadFail P Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadP

Methods

fail :: String -> P a Source

MonadFail ReadP Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadP

Methods

fail :: String -> ReadP a Source

MonadFail ReadPrec Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadPrec

Methods

fail :: String -> ReadPrec a Source

MonadFail IO Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fail

Methods

fail :: String -> IO a Source

MonadFail Maybe Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fail

Methods

fail :: String -> Maybe a Source

MonadFail [] Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fail

Methods

fail :: String -> [a] Source

MonadFail f => MonadFail (Ap f) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

fail :: String -> Ap f a Source

mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () Source

Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM.

mapM_ is just like traverse_, but specialised to monadic actions.

sequence_ :: (Foldable t, Monad m) => t (m a) -> m () Source

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence.

sequence_ is just like sequenceA_, but specialised to monadic actions.

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source

Same as >>=, but with the arguments interchanged.

as >>= f == f =<< as

Folds and traversals

class Foldable (t :: Type -> Type) where Source

The Foldable class represents data structures that can be reduced to a summary value one element at a time. Strict left-associative folds are a good fit for space-efficient reduction, while lazy right-associative folds are a good fit for corecursive iteration, or for folds that short-circuit after processing an initial subsequence of the structure's elements.

Instances can be derived automatically by enabling the DeriveFoldable extension. For example, a derived instance for a binary tree might be:

{-# LANGUAGE DeriveFoldable #-}
data Tree a = Empty
            | Leaf a
            | Node (Tree a) a (Tree a)
    deriving Foldable

A more detailed description can be found in the Overview section of Data.Foldable.

For the class laws see the Laws section of Data.Foldable.

Minimal complete definition

foldMap | foldr

Methods

foldMap :: Monoid m => (a -> m) -> t a -> m Source

Map each element of the structure into a monoid, and combine the results with (<>). This fold is right-associative and lazy in the accumulator. For strict left-associative folds consider foldMap' instead.

Examples
Expand

Basic usage:

>>> foldMap Sum [1, 3, 5]
Sum {getSum = 9}
>>> foldMap Product [1, 3, 5]
Product {getProduct = 15}
>>> foldMap (replicate 3) [1, 2, 3]
[1,1,1,2,2,2,3,3,3]

When a Monoid's (<>) is lazy in its second argument, foldMap can return a result even from an unbounded structure. For example, lazy accumulation enables Data.ByteString.Builder to efficiently serialise large data structures and produce the output incrementally:

>>> import qualified Data.ByteString.Lazy as L
>>> import qualified Data.ByteString.Builder as B
>>> let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20
>>> let lbs = B.toLazyByteString $ foldMap bld [0..]
>>> L.take 64 lbs
"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"

foldr :: (a -> b -> b) -> b -> t a -> b Source

Right-associative fold of a structure, lazy in the accumulator.

In the case of lists, foldr, when applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

Note that since the head of the resulting expression is produced by an application of the operator to the first element of the list, given an operator lazy in its right argument, foldr can produce a terminating expression from an unbounded list.

For a general Foldable structure this should be semantically identical to,

foldr f z = foldr f z . toList
Examples
Expand

Basic usage:

>>> foldr (||) False [False, True, False]
True
>>> foldr (||) False []
False
>>> foldr (\c acc -> acc ++ [c]) "foo" ['a', 'b', 'c', 'd']
"foodcba"
Infinite structures

⚠️ Applying foldr to infinite structures usually doesn't terminate.

It may still terminate under one of the following conditions:

  • the folding function is short-circuiting
  • the folding function is lazy on its second argument
Short-circuiting

(||) short-circuits on True values, so the following terminates because there is a True value finitely far from the left side:

>>> foldr (||) False (True : repeat False)
True

But the following doesn't terminate:

>>> foldr (||) False (repeat False ++ [True])
* Hangs forever *
Laziness in the second argument

Applying foldr to infinite structures terminates when the operator is lazy in its second argument (the initial accumulator is never used in this case, and so could be left undefined, but [] is more clear):

>>> take 5 $ foldr (\i acc -> i : fmap (+3) acc) [] (repeat 1)
[1,4,7,10,13]

foldl :: (b -> a -> b) -> b -> t a -> b Source

Left-associative fold of a structure, lazy in the accumulator. This is rarely what you want, but can work well for structures with efficient right-to-left sequencing and an operator that is lazy in its left argument.

In the case of lists, foldl, when applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

Note that to produce the outermost application of the operator the entire input list must be traversed. Like all left-associative folds, foldl will diverge if given an infinite list.

If you want an efficient strict left-fold, you probably want to use foldl' instead of foldl. The reason for this is that the latter does not force the inner results (e.g. z `f` x1 in the above example) before applying them to the operator (e.g. to (`f` x2)). This results in a thunk chain O(n) elements long, which then must be evaluated from the outside-in.

For a general Foldable structure this should be semantically identical to:

foldl f z = foldl f z . toList
Examples
Expand

The first example is a strict fold, which in practice is best performed with foldl'.

>>> foldl (+) 42 [1,2,3,4]
52

Though the result below is lazy, the input is reversed before prepending it to the initial accumulator, so corecursion begins only after traversing the entire input string.

>>> foldl (\acc c -> c : acc) "abcd" "efgh"
"hgfeabcd"

A left fold of a structure that is infinite on the right cannot terminate, even when for any finite input the fold just returns the initial accumulator:

>>> foldl (\a _ -> a) 0 $ repeat 1
* Hangs forever *

WARNING: When it comes to lists, you always want to use either foldl' or foldr instead.

foldl' :: (b -> a -> b) -> b -> t a -> b Source

Left-associative fold of a structure but with strict application of the operator.

This ensures that each step of the fold is forced to Weak Head Normal Form before being applied, avoiding the collection of thunks that would otherwise occur. This is often what you want to strictly reduce a finite structure to a single strict result (e.g. sum).

For a general Foldable structure this should be semantically identical to,

foldl' f z = foldl' f z . toList

Since: base-4.6.0.0

foldr1 :: (a -> a -> a) -> t a -> a Source

A variant of foldr that has no base case, and thus may only be applied to non-empty structures.

This function is non-total and will raise a runtime exception if the structure happens to be empty.

Examples
Expand

Basic usage:

>>> foldr1 (+) [1..4]
10
>>> foldr1 (+) []
Exception: Prelude.foldr1: empty list
>>> foldr1 (+) Nothing
*** Exception: foldr1: empty structure
>>> foldr1 (-) [1..4]
-2
>>> foldr1 (&&) [True, False, True, True]
False
>>> foldr1 (||) [False, False, True, True]
True
>>> foldr1 (+) [1..]
* Hangs forever *

foldl1 :: (a -> a -> a) -> t a -> a Source

A variant of foldl that has no base case, and thus may only be applied to non-empty structures.

This function is non-total and will raise a runtime exception if the structure happens to be empty.

foldl1 f = foldl1 f . toList
Examples
Expand

Basic usage:

>>> foldl1 (+) [1..4]
10
>>> foldl1 (+) []
*** Exception: Prelude.foldl1: empty list
>>> foldl1 (+) Nothing
*** Exception: foldl1: empty structure
>>> foldl1 (-) [1..4]
-8
>>> foldl1 (&&) [True, False, True, True]
False
>>> foldl1 (||) [False, False, True, True]
True
>>> foldl1 (+) [1..]
* Hangs forever *

elem :: Eq a => a -> t a -> Bool infix 4 Source

Does the element occur in the structure?

Note: elem is often used in infix form.

Examples
Expand

Basic usage:

>>> 3 `elem` []
False
>>> 3 `elem` [1,2]
False
>>> 3 `elem` [1,2,3,4,5]
True

For infinite structures, the default implementation of elem terminates if the sought-after value exists at a finite distance from the left side of the structure:

>>> 3 `elem` [1..]
True
>>> 3 `elem` ([4..] ++ [3])
* Hangs forever *

Since: base-4.8.0.0

maximum :: Ord a => t a -> a Source

The largest element of a non-empty structure. This function is equivalent to foldr1 max, and its behavior on structures with multiple largest elements depends on the relevant implementation of max. For the default implementation of max (max x y = if x <= y then y else x), structure order is used as a tie-breaker: if there are multiple largest elements, the rightmost of them is chosen (this is equivalent to maximumBy compare).

This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.

Examples
Expand

Basic usage:

>>> maximum [1..10]
10
>>> maximum []
*** Exception: Prelude.maximum: empty list
>>> maximum Nothing
*** Exception: maximum: empty structure

WARNING: This function is partial for possibly-empty structures like lists.

Since: base-4.8.0.0

minimum :: Ord a => t a -> a Source

The least element of a non-empty structure. This function is equivalent to foldr1 min, and its behavior on structures with multiple largest elements depends on the relevant implementation of min. For the default implementation of min (min x y = if x <= y then x else y), structure order is used as a tie-breaker: if there are multiple least elements, the leftmost of them is chosen (this is equivalent to minimumBy compare).

This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.

Examples
Expand

Basic usage:

>>> minimum [1..10]
1
>>> minimum []
*** Exception: Prelude.minimum: empty list
>>> minimum Nothing
*** Exception: minimum: empty structure

WARNING: This function is partial for possibly-empty structures like lists.

Since: base-4.8.0.0

sum :: Num a => t a -> a Source

The sum function computes the sum of the numbers of a structure.

Examples
Expand

Basic usage:

>>> sum []
0
>>> sum [42]
42
>>> sum [1..10]
55
>>> sum [4.1, 2.0, 1.7]
7.8
>>> sum [1..]
* Hangs forever *

Since: base-4.8.0.0

product :: Num a => t a -> a Source

The product function computes the product of the numbers of a structure.

Examples
Expand

Basic usage:

>>> product []
1
>>> product [42]
42
>>> product [1..10]
3628800
>>> product [4.1, 2.0, 1.7]
13.939999999999998
>>> product [1..]
* Hangs forever *

Since: base-4.8.0.0

Instances
Instances details
Foldable Complex Source

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Methods

fold :: Monoid m => Complex m -> m Source

foldMap :: Monoid m => (a -> m) -> Complex a -> m Source

foldMap' :: Monoid m => (a -> m) -> Complex a -> m Source

foldr :: (a -> b -> b) -> b -> Complex a -> b Source

foldr' :: (a -> b -> b) -> b -> Complex a -> b Source

foldl :: (b -> a -> b) -> b -> Complex a -> b Source

foldl' :: (b -> a -> b) -> b -> Complex a -> b Source

foldr1 :: (a -> a -> a) -> Complex a -> a Source

foldl1 :: (a -> a -> a) -> Complex a -> a Source

toList :: Complex a -> [a] Source

null :: Complex a -> Bool Source

length :: Complex a -> Int Source

elem :: Eq a => a -> Complex a -> Bool Source

maximum :: Ord a => Complex a -> a Source

minimum :: Ord a => Complex a -> a Source

sum :: Num a => Complex a -> a Source

product :: Num a => Complex a -> a Source

Foldable First Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => First m -> m Source

foldMap :: Monoid m => (a -> m) -> First a -> m Source

foldMap' :: Monoid m => (a -> m) -> First a -> m Source

foldr :: (a -> b -> b) -> b -> First a -> b Source

foldr' :: (a -> b -> b) -> b -> First a -> b Source

foldl :: (b -> a -> b) -> b -> First a -> b Source

foldl' :: (b -> a -> b) -> b -> First a -> b Source

foldr1 :: (a -> a -> a) -> First a -> a Source

foldl1 :: (a -> a -> a) -> First a -> a Source

toList :: First a -> [a] Source

null :: First a -> Bool Source

length :: First a -> Int Source

elem :: Eq a => a -> First a -> Bool Source

maximum :: Ord a => First a -> a Source

minimum :: Ord a => First a -> a Source

sum :: Num a => First a -> a Source

product :: Num a => First a -> a Source

Foldable Last Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Last m -> m Source

foldMap :: Monoid m => (a -> m) -> Last a -> m Source

foldMap' :: Monoid m => (a -> m) -> Last a -> m Source

foldr :: (a -> b -> b) -> b -> Last a -> b Source

foldr' :: (a -> b -> b) -> b -> Last a -> b Source

foldl :: (b -> a -> b) -> b -> Last a -> b Source

foldl' :: (b -> a -> b) -> b -> Last a -> b Source

foldr1 :: (a -> a -> a) -> Last a -> a Source

foldl1 :: (a -> a -> a) -> Last a -> a Source

toList :: Last a -> [a] Source

null :: Last a -> Bool Source

length :: Last a -> Int Source

elem :: Eq a => a -> Last a -> Bool Source

maximum :: Ord a => Last a -> a Source

minimum :: Ord a => Last a -> a Source

sum :: Num a => Last a -> a Source

product :: Num a => Last a -> a Source

Foldable Max Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Max m -> m Source

foldMap :: Monoid m => (a -> m) -> Max a -> m Source

foldMap' :: Monoid m => (a -> m) -> Max a -> m Source

foldr :: (a -> b -> b) -> b -> Max a -> b Source

foldr' :: (a -> b -> b) -> b -> Max a -> b Source

foldl :: (b -> a -> b) -> b -> Max a -> b Source

foldl' :: (b -> a -> b) -> b -> Max a -> b Source

foldr1 :: (a -> a -> a) -> Max a -> a Source

foldl1 :: (a -> a -> a) -> Max a -> a Source

toList :: Max a -> [a] Source

null :: Max a -> Bool Source

length :: Max a -> Int Source

elem :: Eq a => a -> Max a -> Bool Source

maximum :: Ord a => Max a -> a Source

minimum :: Ord a => Max a -> a Source

sum :: Num a => Max a -> a Source

product :: Num a => Max a -> a Source

Foldable Min Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Min m -> m Source

foldMap :: Monoid m => (a -> m) -> Min a -> m Source

foldMap' :: Monoid m => (a -> m) -> Min a -> m Source

foldr :: (a -> b -> b) -> b -> Min a -> b Source

foldr' :: (a -> b -> b) -> b -> Min a -> b Source

foldl :: (b -> a -> b) -> b -> Min a -> b Source

foldl' :: (b -> a -> b) -> b -> Min a -> b Source

foldr1 :: (a -> a -> a) -> Min a -> a Source

foldl1 :: (a -> a -> a) -> Min a -> a Source

toList :: Min a -> [a] Source

null :: Min a -> Bool Source

length :: Min a -> Int Source

elem :: Eq a => a -> Min a -> Bool Source

maximum :: Ord a => Min a -> a Source

minimum :: Ord a => Min a -> a Source

sum :: Num a => Min a -> a Source

product :: Num a => Min a -> a Source

Foldable NonEmpty Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => NonEmpty m -> m Source

foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source

foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m Source

foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source

foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source

foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source

foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source

foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source

foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source

toList :: NonEmpty a -> [a] Source

null :: NonEmpty a -> Bool Source

length :: NonEmpty a -> Int Source

elem :: Eq a => a -> NonEmpty a -> Bool Source

maximum :: Ord a => NonEmpty a -> a Source

minimum :: Ord a => NonEmpty a -> a Source

sum :: Num a => NonEmpty a -> a Source

product :: Num a => NonEmpty a -> a Source

Foldable Identity Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Methods

fold :: Monoid m => Identity m -> m Source

foldMap :: Monoid m => (a -> m) -> Identity a -> m Source

foldMap' :: Monoid m => (a -> m) -> Identity a -> m Source

foldr :: (a -> b -> b) -> b -> Identity a -> b Source

foldr' :: (a -> b -> b) -> b -> Identity a -> b Source

foldl :: (b -> a -> b) -> b -> Identity a -> b Source

foldl' :: (b -> a -> b) -> b -> Identity a -> b Source

foldr1 :: (a -> a -> a) -> Identity a -> a Source

foldl1 :: (a -> a -> a) -> Identity a -> a Source

toList :: Identity a -> [a] Source

null :: Identity a -> Bool Source

length :: Identity a -> Int Source

elem :: Eq a => a -> Identity a -> Bool Source

maximum :: Ord a => Identity a -> a Source

minimum :: Ord a => Identity a -> a Source

sum :: Num a => Identity a -> a Source

product :: Num a => Identity a -> a Source

Foldable First Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => First m -> m Source

foldMap :: Monoid m => (a -> m) -> First a -> m Source

foldMap' :: Monoid m => (a -> m) -> First a -> m Source

foldr :: (a -> b -> b) -> b -> First a -> b Source

foldr' :: (a -> b -> b) -> b -> First a -> b Source

foldl :: (b -> a -> b) -> b -> First a -> b Source

foldl' :: (b -> a -> b) -> b -> First a -> b Source

foldr1 :: (a -> a -> a) -> First a -> a Source

foldl1 :: (a -> a -> a) -> First a -> a Source

toList :: First a -> [a] Source

null :: First a -> Bool Source

length :: First a -> Int Source

elem :: Eq a => a -> First a -> Bool Source

maximum :: Ord a => First a -> a Source

minimum :: Ord a => First a -> a Source

sum :: Num a => First a -> a Source

product :: Num a => First a -> a Source

Foldable Last Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Last m -> m Source

foldMap :: Monoid m => (a -> m) -> Last a -> m Source

foldMap' :: Monoid m => (a -> m) -> Last a -> m Source

foldr :: (a -> b -> b) -> b -> Last a -> b Source

foldr' :: (a -> b -> b) -> b -> Last a -> b Source

foldl :: (b -> a -> b) -> b -> Last a -> b Source

foldl' :: (b -> a -> b) -> b -> Last a -> b Source

foldr1 :: (a -> a -> a) -> Last a -> a Source

foldl1 :: (a -> a -> a) -> Last a -> a Source

toList :: Last a -> [a] Source

null :: Last a -> Bool Source

length :: Last a -> Int Source

elem :: Eq a => a -> Last a -> Bool Source

maximum :: Ord a => Last a -> a Source

minimum :: Ord a => Last a -> a Source

sum :: Num a => Last a -> a Source

product :: Num a => Last a -> a Source

Foldable Down Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Down m -> m Source

foldMap :: Monoid m => (a -> m) -> Down a -> m Source

foldMap' :: Monoid m => (a -> m) -> Down a -> m Source

foldr :: (a -> b -> b) -> b -> Down a -> b Source

foldr' :: (a -> b -> b) -> b -> Down a -> b Source

foldl :: (b -> a -> b) -> b -> Down a -> b Source

foldl' :: (b -> a -> b) -> b -> Down a -> b Source

foldr1 :: (a -> a -> a) -> Down a -> a Source

foldl1 :: (a -> a -> a) -> Down a -> a Source

toList :: Down a -> [a] Source

null :: Down a -> Bool Source

length :: Down a -> Int Source

elem :: Eq a => a -> Down a -> Bool Source

maximum :: Ord a => Down a -> a Source

minimum :: Ord a => Down a -> a Source

sum :: Num a => Down a -> a Source

product :: Num a => Down a -> a Source

Foldable Dual Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Dual m -> m Source

foldMap :: Monoid m => (a -> m) -> Dual a -> m Source

foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source

foldr :: (a -> b -> b) -> b -> Dual a -> b Source

foldr' :: (a -> b -> b) -> b -> Dual a -> b Source

foldl :: (b -> a -> b) -> b -> Dual a -> b Source

foldl' :: (b -> a -> b) -> b -> Dual a -> b Source

foldr1 :: (a -> a -> a) -> Dual a -> a Source

foldl1 :: (a -> a -> a) -> Dual a -> a Source

toList :: Dual a -> [a] Source

null :: Dual a -> Bool Source

length :: Dual a -> Int Source

elem :: Eq a => a -> Dual a -> Bool Source

maximum :: Ord a => Dual a -> a Source

minimum :: Ord a => Dual a -> a Source

sum :: Num a => Dual a -> a Source

product :: Num a => Dual a -> a Source

Foldable Product Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Product m -> m Source

foldMap :: Monoid m => (a -> m) -> Product a -> m Source

foldMap' :: Monoid m => (a -> m) -> Product a -> m Source

foldr :: (a -> b -> b) -> b -> Product a -> b Source

foldr' :: (a -> b -> b) -> b -> Product a -> b Source

foldl :: (b -> a -> b) -> b -> Product a -> b Source

foldl' :: (b -> a -> b) -> b -> Product a -> b Source

foldr1 :: (a -> a -> a) -> Product a -> a Source

foldl1 :: (a -> a -> a) -> Product a -> a Source

toList :: Product a -> [a] Source

null :: Product a -> Bool Source

length :: Product a -> Int Source

elem :: Eq a => a -> Product a -> Bool Source

maximum :: Ord a => Product a -> a Source

minimum :: Ord a => Product a -> a Source

sum :: Num a => Product a -> a Source

product :: Num a => Product a -> a Source

Foldable Sum Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Sum m -> m Source

foldMap :: Monoid m => (a -> m) -> Sum a -> m Source

foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source

foldr :: (a -> b -> b) -> b -> Sum a -> b Source

foldr' :: (a -> b -> b) -> b -> Sum a -> b Source

foldl :: (b -> a -> b) -> b -> Sum a -> b Source

foldl' :: (b -> a -> b) -> b -> Sum a -> b Source

foldr1 :: (a -> a -> a) -> Sum a -> a Source

foldl1 :: (a -> a -> a) -> Sum a -> a Source

toList :: Sum a -> [a] Source

null :: Sum a -> Bool Source

length :: Sum a -> Int Source

elem :: Eq a => a -> Sum a -> Bool Source

maximum :: Ord a => Sum a -> a Source

minimum :: Ord a => Sum a -> a Source

sum :: Num a => Sum a -> a Source

product :: Num a => Sum a -> a Source

Foldable ZipList Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

fold :: Monoid m => ZipList m -> m Source

foldMap :: Monoid m => (a -> m) -> ZipList a -> m Source

foldMap' :: Monoid m => (a -> m) -> ZipList a -> m Source

foldr :: (a -> b -> b) -> b -> ZipList a -> b Source

foldr' :: (a -> b -> b) -> b -> ZipList a -> b Source

foldl :: (b -> a -> b) -> b -> ZipList a -> b Source

foldl' :: (b -> a -> b) -> b -> ZipList a -> b Source

foldr1 :: (a -> a -> a) -> ZipList a -> a Source

foldl1 :: (a -> a -> a) -> ZipList a -> a Source

toList :: ZipList a -> [a] Source

null :: ZipList a -> Bool Source

length :: ZipList a -> Int Source

elem :: Eq a => a -> ZipList a -> Bool Source

maximum :: Ord a => ZipList a -> a Source

minimum :: Ord a => ZipList a -> a Source

sum :: Num a => ZipList a -> a Source

product :: Num a => ZipList a -> a Source

Foldable Par1 Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Par1 m -> m Source

foldMap :: Monoid m => (a -> m) -> Par1 a -> m Source

foldMap' :: Monoid m => (a -> m) -> Par1 a -> m Source

foldr :: (a -> b -> b) -> b -> Par1 a -> b Source

foldr' :: (a -> b -> b) -> b -> Par1 a -> b Source

foldl :: (b -> a -> b) -> b -> Par1 a -> b Source

foldl' :: (b -> a -> b) -> b -> Par1 a -> b Source

foldr1 :: (a -> a -> a) -> Par1 a -> a Source

foldl1 :: (a -> a -> a) -> Par1 a -> a Source

toList :: Par1 a -> [a] Source

null :: Par1 a -> Bool Source

length :: Par1 a -> Int Source

elem :: Eq a => a -> Par1 a -> Bool Source

maximum :: Ord a => Par1 a -> a Source

minimum :: Ord a => Par1 a -> a Source

sum :: Num a => Par1 a -> a Source

product :: Num a => Par1 a -> a Source

Foldable TyVarBndr Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

fold :: Monoid m => TyVarBndr m -> m Source

foldMap :: Monoid m => (a -> m) -> TyVarBndr a -> m Source

foldMap' :: Monoid m => (a -> m) -> TyVarBndr a -> m Source

foldr :: (a -> b -> b) -> b -> TyVarBndr a -> b Source

foldr' :: (a -> b -> b) -> b -> TyVarBndr a -> b Source

foldl :: (b -> a -> b) -> b -> TyVarBndr a -> b Source

foldl' :: (b -> a -> b) -> b -> TyVarBndr a -> b Source

foldr1 :: (a -> a -> a) -> TyVarBndr a -> a Source

foldl1 :: (a -> a -> a) -> TyVarBndr a -> a Source

toList :: TyVarBndr a -> [a] Source

null :: TyVarBndr a -> Bool Source

length :: TyVarBndr a -> Int Source

elem :: Eq a => a -> TyVarBndr a -> Bool Source

maximum :: Ord a => TyVarBndr a -> a Source

minimum :: Ord a => TyVarBndr a -> a Source

sum :: Num a => TyVarBndr a -> a Source

product :: Num a => TyVarBndr a -> a Source

Foldable Maybe Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Maybe m -> m Source

foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source

foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source

foldr :: (a -> b -> b) -> b -> Maybe a -> b Source

foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source

foldl :: (b -> a -> b) -> b -> Maybe a -> b Source

foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source

foldr1 :: (a -> a -> a) -> Maybe a -> a Source

foldl1 :: (a -> a -> a) -> Maybe a -> a Source

toList :: Maybe a -> [a] Source

null :: Maybe a -> Bool Source

length :: Maybe a -> Int Source

elem :: Eq a => a -> Maybe a -> Bool Source

maximum :: Ord a => Maybe a -> a Source

minimum :: Ord a => Maybe a -> a Source

sum :: Num a => Maybe a -> a Source

product :: Num a => Maybe a -> a Source

Foldable Solo Source

Since: base-4.15

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Solo m -> m Source

foldMap :: Monoid m => (a -> m) -> Solo a -> m Source

foldMap' :: Monoid m => (a -> m) -> Solo a -> m Source

foldr :: (a -> b -> b) -> b -> Solo a -> b Source

foldr' :: (a -> b -> b) -> b -> Solo a -> b Source

foldl :: (b -> a -> b) -> b -> Solo a -> b Source

foldl' :: (b -> a -> b) -> b -> Solo a -> b Source

foldr1 :: (a -> a -> a) -> Solo a -> a Source

foldl1 :: (a -> a -> a) -> Solo a -> a Source

toList :: Solo a -> [a] Source

null :: Solo a -> Bool Source

length :: Solo a -> Int Source

elem :: Eq a => a -> Solo a -> Bool Source

maximum :: Ord a => Solo a -> a Source

minimum :: Ord a => Solo a -> a Source

sum :: Num a => Solo a -> a Source

product :: Num a => Solo a -> a Source

Foldable [] Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => [m] -> m Source

foldMap :: Monoid m => (a -> m) -> [a] -> m Source

foldMap' :: Monoid m => (a -> m) -> [a] -> m Source

foldr :: (a -> b -> b) -> b -> [a] -> b Source

foldr' :: (a -> b -> b) -> b -> [a] -> b Source

foldl :: (b -> a -> b) -> b -> [a] -> b Source

foldl' :: (b -> a -> b) -> b -> [a] -> b Source

foldr1 :: (a -> a -> a) -> [a] -> a Source

foldl1 :: (a -> a -> a) -> [a] -> a Source

toList :: [a] -> [a] Source

null :: [a] -> Bool Source

length :: [a] -> Int Source

elem :: Eq a => a -> [a] -> Bool Source

maximum :: Ord a => [a] -> a Source

minimum :: Ord a => [a] -> a Source

sum :: Num a => [a] -> a Source

product :: Num a => [a] -> a Source

Foldable (Arg a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Arg a m -> m Source

foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source

foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source

foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source

foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source

foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source

foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source

foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source

foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source

toList :: Arg a a0 -> [a0] Source

null :: Arg a a0 -> Bool Source

length :: Arg a a0 -> Int Source

elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source

maximum :: Ord a0 => Arg a a0 -> a0 Source

minimum :: Ord a0 => Arg a a0 -> a0 Source

sum :: Num a0 => Arg a a0 -> a0 Source

product :: Num a0 => Arg a a0 -> a0 Source

Foldable (Array i) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Array i m -> m Source

foldMap :: Monoid m => (a -> m) -> Array i a -> m Source

foldMap' :: Monoid m => (a -> m) -> Array i a -> m Source

foldr :: (a -> b -> b) -> b -> Array i a -> b Source

foldr' :: (a -> b -> b) -> b -> Array i a -> b Source

foldl :: (b -> a -> b) -> b -> Array i a -> b Source

foldl' :: (b -> a -> b) -> b -> Array i a -> b Source

foldr1 :: (a -> a -> a) -> Array i a -> a Source

foldl1 :: (a -> a -> a) -> Array i a -> a Source

toList :: Array i a -> [a] Source

null :: Array i a -> Bool Source

length :: Array i a -> Int Source

elem :: Eq a => a -> Array i a -> Bool Source

maximum :: Ord a => Array i a -> a Source

minimum :: Ord a => Array i a -> a Source

sum :: Num a => Array i a -> a Source

product :: Num a => Array i a -> a Source

Foldable (Either a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Either a m -> m Source

foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source

foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source

foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source

foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source

foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source

foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source

foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source

foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source

toList :: Either a a0 -> [a0] Source

null :: Either a a0 -> Bool Source

length :: Either a a0 -> Int Source

elem :: Eq a0 => a0 -> Either a a0 -> Bool Source

maximum :: Ord a0 => Either a a0 -> a0 Source

minimum :: Ord a0 => Either a a0 -> a0 Source

sum :: Num a0 => Either a a0 -> a0 Source

product :: Num a0 => Either a a0 -> a0 Source

Foldable (Proxy :: Type -> Type) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Proxy m -> m Source

foldMap :: Monoid m => (a -> m) -> Proxy a -> m Source

foldMap' :: Monoid m => (a -> m) -> Proxy a -> m Source

foldr :: (a -> b -> b) -> b -> Proxy a -> b Source

foldr' :: (a -> b -> b) -> b -> Proxy a -> b Source

foldl :: (b -> a -> b) -> b -> Proxy a -> b Source

foldl' :: (b -> a -> b) -> b -> Proxy a -> b Source

foldr1 :: (a -> a -> a) -> Proxy a -> a Source

foldl1 :: (a -> a -> a) -> Proxy a -> a Source

toList :: Proxy a -> [a] Source

null :: Proxy a -> Bool Source

length :: Proxy a -> Int Source

elem :: Eq a => a -> Proxy a -> Bool Source

maximum :: Ord a => Proxy a -> a Source

minimum :: Ord a => Proxy a -> a Source

sum :: Num a => Proxy a -> a Source

product :: Num a => Proxy a -> a Source

Foldable (U1 :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => U1 m -> m Source

foldMap :: Monoid m => (a -> m) -> U1 a -> m Source

foldMap' :: Monoid m => (a -> m) -> U1 a -> m Source

foldr :: (a -> b -> b) -> b -> U1 a -> b Source

foldr' :: (a -> b -> b) -> b -> U1 a -> b Source

foldl :: (b -> a -> b) -> b -> U1 a -> b Source

foldl' :: (b -> a -> b) -> b -> U1 a -> b Source

foldr1 :: (a -> a -> a) -> U1 a -> a Source

foldl1 :: (a -> a -> a) -> U1 a -> a Source

toList :: U1 a -> [a] Source

null :: U1 a -> Bool Source

length :: U1 a -> Int Source

elem :: Eq a => a -> U1 a -> Bool Source

maximum :: Ord a => U1 a -> a Source

minimum :: Ord a => U1 a -> a Source

sum :: Num a => U1 a -> a Source

product :: Num a => U1 a -> a Source

Foldable (UAddr :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UAddr m -> m Source

foldMap :: Monoid m => (a -> m) -> UAddr a -> m Source

foldMap' :: Monoid m => (a -> m) -> UAddr a -> m Source

foldr :: (a -> b -> b) -> b -> UAddr a -> b Source

foldr' :: (a -> b -> b) -> b -> UAddr a -> b Source

foldl :: (b -> a -> b) -> b -> UAddr a -> b Source

foldl' :: (b -> a -> b) -> b -> UAddr a -> b Source

foldr1 :: (a -> a -> a) -> UAddr a -> a Source

foldl1 :: (a -> a -> a) -> UAddr a -> a Source

toList :: UAddr a -> [a] Source

null :: UAddr a -> Bool Source

length :: UAddr a -> Int Source

elem :: Eq a => a -> UAddr a -> Bool Source

maximum :: Ord a => UAddr a -> a Source

minimum :: Ord a => UAddr a -> a Source

sum :: Num a => UAddr a -> a Source

product :: Num a => UAddr a -> a Source

Foldable (UChar :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UChar m -> m Source

foldMap :: Monoid m => (a -> m) -> UChar a -> m Source

foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source

foldr :: (a -> b -> b) -> b -> UChar a -> b Source

foldr' :: (a -> b -> b) -> b -> UChar a -> b Source

foldl :: (b -> a -> b) -> b -> UChar a -> b Source

foldl' :: (b -> a -> b) -> b -> UChar a -> b Source

foldr1 :: (a -> a -> a) -> UChar a -> a Source

foldl1 :: (a -> a -> a) -> UChar a -> a Source

toList :: UChar a -> [a] Source

null :: UChar a -> Bool Source

length :: UChar a -> Int Source

elem :: Eq a => a -> UChar a -> Bool Source

maximum :: Ord a => UChar a -> a Source

minimum :: Ord a => UChar a -> a Source

sum :: Num a => UChar a -> a Source

product :: Num a => UChar a -> a Source

Foldable (UDouble :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UDouble m -> m Source

foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source

foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source

foldr :: (a -> b -> b) -> b -> UDouble a -> b Source

foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source

foldl :: (b -> a -> b) -> b -> UDouble a -> b Source

foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source

foldr1 :: (a -> a -> a) -> UDouble a -> a Source

foldl1 :: (a -> a -> a) -> UDouble a -> a Source

toList :: UDouble a -> [a] Source

null :: UDouble a -> Bool Source

length :: UDouble a -> Int Source

elem :: Eq a => a -> UDouble a -> Bool Source

maximum :: Ord a => UDouble a -> a Source

minimum :: Ord a => UDouble a -> a Source

sum :: Num a => UDouble a -> a Source

product :: Num a => UDouble a -> a Source

Foldable (UFloat :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UFloat m -> m Source

foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source

foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source

foldr :: (a -> b -> b) -> b -> UFloat a -> b Source

foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source

foldl :: (b -> a -> b) -> b -> UFloat a -> b Source

foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source

foldr1 :: (a -> a -> a) -> UFloat a -> a Source

foldl1 :: (a -> a -> a) -> UFloat a -> a Source

toList :: UFloat a -> [a] Source

null :: UFloat a -> Bool Source

length :: UFloat a -> Int Source

elem :: Eq a => a -> UFloat a -> Bool Source

maximum :: Ord a => UFloat a -> a Source

minimum :: Ord a => UFloat a -> a Source

sum :: Num a => UFloat a -> a Source

product :: Num a => UFloat a -> a Source

Foldable (UInt :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UInt m -> m Source

foldMap :: Monoid m => (a -> m) -> UInt a -> m Source

foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source

foldr :: (a -> b -> b) -> b -> UInt a -> b Source

foldr' :: (a -> b -> b) -> b -> UInt a -> b Source

foldl :: (b -> a -> b) -> b -> UInt a -> b Source

foldl' :: (b -> a -> b) -> b -> UInt a -> b Source

foldr1 :: (a -> a -> a) -> UInt a -> a Source

foldl1 :: (a -> a -> a) -> UInt a -> a Source

toList :: UInt a -> [a] Source

null :: UInt a -> Bool Source

length :: UInt a -> Int Source

elem :: Eq a => a -> UInt a -> Bool Source

maximum :: Ord a => UInt a -> a Source

minimum :: Ord a => UInt a -> a Source

sum :: Num a => UInt a -> a Source

product :: Num a => UInt a -> a Source

Foldable (UWord :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UWord m -> m Source

foldMap :: Monoid m => (a -> m) -> UWord a -> m Source

foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source

foldr :: (a -> b -> b) -> b -> UWord a -> b Source

foldr' :: (a -> b -> b) -> b -> UWord a -> b Source

foldl :: (b -> a -> b) -> b -> UWord a -> b Source

foldl' :: (b -> a -> b) -> b -> UWord a -> b Source

foldr1 :: (a -> a -> a) -> UWord a -> a Source

foldl1 :: (a -> a -> a) -> UWord a -> a Source

toList :: UWord a -> [a] Source

null :: UWord a -> Bool Source

length :: UWord a -> Int Source

elem :: Eq a => a -> UWord a -> Bool Source

maximum :: Ord a => UWord a -> a Source

minimum :: Ord a => UWord a -> a Source

sum :: Num a => UWord a -> a Source

product :: Num a => UWord a -> a Source

Foldable (V1 :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => V1 m -> m Source

foldMap :: Monoid m => (a -> m) -> V1 a -> m Source

foldMap' :: Monoid m => (a -> m) -> V1 a -> m Source

foldr :: (a -> b -> b) -> b -> V1 a -> b Source

foldr' :: (a -> b -> b) -> b -> V1 a -> b Source

foldl :: (b -> a -> b) -> b -> V1 a -> b Source

foldl' :: (b -> a -> b) -> b -> V1 a -> b Source

foldr1 :: (a -> a -> a) -> V1 a -> a Source

foldl1 :: (a -> a -> a) -> V1 a -> a Source

toList :: V1 a -> [a] Source

null :: V1 a -> Bool Source

length :: V1 a -> Int Source

elem :: Eq a => a -> V1 a -> Bool Source

maximum :: Ord a => V1 a -> a Source

minimum :: Ord a => V1 a -> a Source

sum :: Num a => V1 a -> a Source

product :: Num a => V1 a -> a Source

Foldable ((,) a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => (a, m) -> m Source

foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m Source

foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m Source

foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b Source

foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b Source

foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b Source

foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b Source

foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source

foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source

toList :: (a, a0) -> [a0] Source

null :: (a, a0) -> Bool Source

length :: (a, a0) -> Int Source

elem :: Eq a0 => a0 -> (a, a0) -> Bool Source

maximum :: Ord a0 => (a, a0) -> a0 Source

minimum :: Ord a0 => (a, a0) -> a0 Source

sum :: Num a0 => (a, a0) -> a0 Source

product :: Num a0 => (a, a0) -> a0 Source

Foldable (Const m :: Type -> Type) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

fold :: Monoid m0 => Const m m0 -> m0 Source

foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source

foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source

foldr :: (a -> b -> b) -> b -> Const m a -> b Source

foldr' :: (a -> b -> b) -> b -> Const m a -> b Source

foldl :: (b -> a -> b) -> b -> Const m a -> b Source

foldl' :: (b -> a -> b) -> b -> Const m a -> b Source

foldr1 :: (a -> a -> a) -> Const m a -> a Source

foldl1 :: (a -> a -> a) -> Const m a -> a Source

toList :: Const m a -> [a] Source

null :: Const m a -> Bool Source

length :: Const m a -> Int Source

elem :: Eq a => a -> Const m a -> Bool Source

maximum :: Ord a => Const m a -> a Source

minimum :: Ord a => Const m a -> a Source

sum :: Num a => Const m a -> a Source

product :: Num a => Const m a -> a Source

Foldable f => Foldable (Ap f) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Ap f m -> m Source

foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source

foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source

foldr :: (a -> b -> b) -> b -> Ap f a -> b Source

foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source

foldl :: (b -> a -> b) -> b -> Ap f a -> b Source

foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source

foldr1 :: (a -> a -> a) -> Ap f a -> a Source

foldl1 :: (a -> a -> a) -> Ap f a -> a Source

toList :: Ap f a -> [a] Source

null :: Ap f a -> Bool Source

length :: Ap f a -> Int Source

elem :: Eq a => a -> Ap f a -> Bool Source

maximum :: Ord a => Ap f a -> a Source

minimum :: Ord a => Ap f a -> a Source

sum :: Num a => Ap f a -> a Source

product :: Num a => Ap f a -> a Source

Foldable f => Foldable (Alt f) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Alt f m -> m Source

foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source

foldMap' :: Monoid m => (a -> m) -> Alt f a -> m Source

foldr :: (a -> b -> b) -> b -> Alt f a -> b Source

foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source

foldl :: (b -> a -> b) -> b -> Alt f a -> b Source

foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source

foldr1 :: (a -> a -> a) -> Alt f a -> a Source

foldl1 :: (a -> a -> a) -> Alt f a -> a Source

toList :: Alt f a -> [a] Source

null :: Alt f a -> Bool Source

length :: Alt f a -> Int Source

elem :: Eq a => a -> Alt f a -> Bool Source

maximum :: Ord a => Alt f a -> a Source

minimum :: Ord a => Alt f a -> a Source

sum :: Num a => Alt f a -> a Source

product :: Num a => Alt f a -> a Source

Foldable f => Foldable (Rec1 f) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Rec1 f m -> m Source

foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m Source

foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m Source

foldr :: (a -> b -> b) -> b -> Rec1 f a -> b Source

foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b Source

foldl :: (b -> a -> b) -> b -> Rec1 f a -> b Source

foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b Source

foldr1 :: (a -> a -> a) -> Rec1 f a -> a Source

foldl1 :: (a -> a -> a) -> Rec1 f a -> a Source

toList :: Rec1 f a -> [a] Source

null :: Rec1 f a -> Bool Source

length :: Rec1 f a -> Int Source

elem :: Eq a => a -> Rec1 f a -> Bool Source

maximum :: Ord a => Rec1 f a -> a Source

minimum :: Ord a => Rec1 f a -> a Source

sum :: Num a => Rec1 f a -> a Source

product :: Num a => Rec1 f a -> a Source

(Foldable f, Foldable g) => Foldable (Product f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

fold :: Monoid m => Product f g m -> m Source

foldMap :: Monoid m => (a -> m) -> Product f g a -> m Source

foldMap' :: Monoid m => (a -> m) -> Product f g a -> m Source

foldr :: (a -> b -> b) -> b -> Product f g a -> b Source

foldr' :: (a -> b -> b) -> b -> Product f g a -> b Source

foldl :: (b -> a -> b) -> b -> Product f g a -> b Source

foldl' :: (b -> a -> b) -> b -> Product f g a -> b Source

foldr1 :: (a -> a -> a) -> Product f g a -> a Source

foldl1 :: (a -> a -> a) -> Product f g a -> a Source

toList :: Product f g a -> [a] Source

null :: Product f g a -> Bool Source

length :: Product f g a -> Int Source

elem :: Eq a => a -> Product f g a -> Bool Source

maximum :: Ord a => Product f g a -> a Source

minimum :: Ord a => Product f g a -> a Source

sum :: Num a => Product f g a -> a Source

product :: Num a => Product f g a -> a Source

(Foldable f, Foldable g) => Foldable (Sum f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

Methods

fold :: Monoid m => Sum f g m -> m Source

foldMap :: Monoid m => (a -> m) -> Sum f g a -> m Source

foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m Source

foldr :: (a -> b -> b) -> b -> Sum f g a -> b Source

foldr' :: (a -> b -> b) -> b -> Sum f g a -> b Source

foldl :: (b -> a -> b) -> b -> Sum f g a -> b Source

foldl' :: (b -> a -> b) -> b -> Sum f g a -> b Source

foldr1 :: (a -> a -> a) -> Sum f g a -> a Source

foldl1 :: (a -> a -> a) -> Sum f g a -> a Source

toList :: Sum f g a -> [a] Source

null :: Sum f g a -> Bool Source

length :: Sum f g a -> Int Source

elem :: Eq a => a -> Sum f g a -> Bool Source

maximum :: Ord a => Sum f g a -> a Source

minimum :: Ord a => Sum f g a -> a Source

sum :: Num a => Sum f g a -> a Source

product :: Num a => Sum f g a -> a Source

(Foldable f, Foldable g) => Foldable (f :*: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => (f :*: g) m -> m Source

foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m Source

foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m Source

foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b Source

foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b Source

foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b Source

foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b Source

foldr1 :: (a -> a -> a) -> (f :*: g) a -> a Source

foldl1 :: (a -> a -> a) -> (f :*: g) a -> a Source

toList :: (f :*: g) a -> [a] Source

null :: (f :*: g) a -> Bool Source

length :: (f :*: g) a -> Int Source

elem :: Eq a => a -> (f :*: g) a -> Bool Source

maximum :: Ord a => (f :*: g) a -> a Source

minimum :: Ord a => (f :*: g) a -> a Source

sum :: Num a => (f :*: g) a -> a Source

product :: Num a => (f :*: g) a -> a Source

(Foldable f, Foldable g) => Foldable (f :+: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => (f :+: g) m -> m Source

foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m Source

foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m Source

foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b Source

foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b Source

foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b Source

foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b Source

foldr1 :: (a -> a -> a) -> (f :+: g) a -> a Source

foldl1 :: (a -> a -> a) -> (f :+: g) a -> a Source

toList :: (f :+: g) a -> [a] Source

null :: (f :+: g) a -> Bool Source

length :: (f :+: g) a -> Int Source

elem :: Eq a => a -> (f :+: g) a -> Bool Source

maximum :: Ord a => (f :+: g) a -> a Source

minimum :: Ord a => (f :+: g) a -> a Source

sum :: Num a => (f :+: g) a -> a Source

product :: Num a => (f :+: g) a -> a Source

Foldable (K1 i c :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => K1 i c m -> m Source

foldMap :: Monoid m => (a -> m) -> K1 i c a -> m Source

foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m Source

foldr :: (a -> b -> b) -> b -> K1 i c a -> b Source

foldr' :: (a -> b -> b) -> b -> K1 i c a -> b Source

foldl :: (b -> a -> b) -> b -> K1 i c a -> b Source

foldl' :: (b -> a -> b) -> b -> K1 i c a -> b Source

foldr1 :: (a -> a -> a) -> K1 i c a -> a Source

foldl1 :: (a -> a -> a) -> K1 i c a -> a Source

toList :: K1 i c a -> [a] Source

null :: K1 i c a -> Bool Source

length :: K1 i c a -> Int Source

elem :: Eq a => a -> K1 i c a -> Bool Source

maximum :: Ord a => K1 i c a -> a Source

minimum :: Ord a => K1 i c a -> a Source

sum :: Num a => K1 i c a -> a Source

product :: Num a => K1 i c a -> a Source

(Foldable f, Foldable g) => Foldable (Compose f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

fold :: Monoid m => Compose f g m -> m Source

foldMap :: Monoid m => (a -> m) -> Compose f g a -> m Source

foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m Source

foldr :: (a -> b -> b) -> b -> Compose f g a -> b Source

foldr' :: (a -> b -> b) -> b -> Compose f g a -> b Source

foldl :: (b -> a -> b) -> b -> Compose f g a -> b Source

foldl' :: (b -> a -> b) -> b -> Compose f g a -> b Source

foldr1 :: (a -> a -> a) -> Compose f g a -> a Source

foldl1 :: (a -> a -> a) -> Compose f g a -> a Source

toList :: Compose f g a -> [a] Source

null :: Compose f g a -> Bool Source

length :: Compose f g a -> Int Source

elem :: Eq a => a -> Compose f g a -> Bool Source

maximum :: Ord a => Compose f g a -> a Source

minimum :: Ord a => Compose f g a -> a Source

sum :: Num a => Compose f g a -> a Source

product :: Num a => Compose f g a -> a Source

(Foldable f, Foldable g) => Foldable (f :.: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => (f :.: g) m -> m Source

foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m Source

foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m Source

foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b Source

foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b Source

foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b Source

foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b Source

foldr1 :: (a -> a -> a) -> (f :.: g) a -> a Source

foldl1 :: (a -> a -> a) -> (f :.: g) a -> a Source

toList :: (f :.: g) a -> [a] Source

null :: (f :.: g) a -> Bool Source

length :: (f :.: g) a -> Int Source

elem :: Eq a => a -> (f :.: g) a -> Bool Source

maximum :: Ord a => (f :.: g) a -> a Source

minimum :: Ord a => (f :.: g) a -> a Source

sum :: Num a => (f :.: g) a -> a Source

product :: Num a => (f :.: g) a -> a Source

Foldable f => Foldable (M1 i c f) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => M1 i c f m -> m Source

foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m Source

foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m Source

foldr :: (a -> b -> b) -> b -> M1 i c f a -> b Source

foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b Source

foldl :: (b -> a -> b) -> b -> M1 i c f a -> b Source

foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b Source

foldr1 :: (a -> a -> a) -> M1 i c f a -> a Source

foldl1 :: (a -> a -> a) -> M1 i c f a -> a Source

toList :: M1 i c f a -> [a] Source

null :: M1 i c f a -> Bool Source

length :: M1 i c f a -> Int Source

elem :: Eq a => a -> M1 i c f a -> Bool Source

maximum :: Ord a => M1 i c f a -> a Source

minimum :: Ord a => M1 i c f a -> a Source

sum :: Num a => M1 i c f a -> a Source

product :: Num a => M1 i c f a -> a Source

class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where Source

Functors representing data structures that can be transformed to structures of the same shape by performing an Applicative (or, therefore, Monad) action on each element from left to right.

A more detailed description of what same shape means, the various methods, how traversals are constructed, and example advanced use-cases can be found in the Overview section of Data.Traversable.

For the class laws see the Laws section of Data.Traversable.

Minimal complete definition

traverse | sequenceA

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b) Source

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see traverse_.

Examples
Expand

Basic usage:

In the first two examples we show each evaluated action mapping to the output structure.

>>> traverse Just [1,2,3,4]
Just [1,2,3,4]
>>> traverse id [Right 1, Right 2, Right 3, Right 4]
Right [1,2,3,4]

In the next examples, we show that Nothing and Left values short circuit the created structure.

>>> traverse (const Nothing) [1,2,3,4]
Nothing
>>> traverse (\x -> if odd x then Just x else Nothing)  [1,2,3,4]
Nothing
>>> traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]
Left 0

sequenceA :: Applicative f => t (f a) -> f (t a) Source

Evaluate each action in the structure from left to right, and collect the results. For a version that ignores the results see sequenceA_.

Examples
Expand

Basic usage:

For the first two examples we show sequenceA fully evaluating a a structure and collecting the results.

>>> sequenceA [Just 1, Just 2, Just 3]
Just [1,2,3]
>>> sequenceA [Right 1, Right 2, Right 3]
Right [1,2,3]

The next two example show Nothing and Just will short circuit the resulting structure if present in the input. For more context, check the Traversable instances for Either and Maybe.

>>> sequenceA [Just 1, Just 2, Just 3, Nothing]
Nothing
>>> sequenceA [Right 1, Right 2, Right 3, Left 4]
Left 4

mapM :: Monad m => (a -> m b) -> t a -> m (t b) Source

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see mapM_.

Examples
Expand

mapM is literally a traverse with a type signature restricted to Monad. Its implementation may be more efficient due to additional power of Monad.

sequence :: Monad m => t (m a) -> m (t a) Source

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.

Examples
Expand

Basic usage:

The first two examples are instances where the input and and output of sequence are isomorphic.

>>> sequence $ Right [1,2,3,4]
[Right 1,Right 2,Right 3,Right 4]
>>> sequence $ [Right 1,Right 2,Right 3,Right 4]
Right [1,2,3,4]

The following examples demonstrate short circuit behavior for sequence.

>>> sequence $ Left [1,2,3,4]
Left [1,2,3,4]
>>> sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]
Left 0
Instances
Instances details
Traversable Complex Source

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Methods

traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) Source

sequenceA :: Applicative f => Complex (f a) -> f (Complex a) Source

mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) Source

sequence :: Monad m => Complex (m a) -> m (Complex a) Source

Traversable First Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source

sequenceA :: Applicative f => First (f a) -> f (First a) Source

mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source

sequence :: Monad m => First (m a) -> m (First a) Source

Traversable Last Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source

sequenceA :: Applicative f => Last (f a) -> f (Last a) Source

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source

sequence :: Monad m => Last (m a) -> m (Last a) Source

Traversable Max Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) Source

sequenceA :: Applicative f => Max (f a) -> f (Max a) Source

mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) Source

sequence :: Monad m => Max (m a) -> m (Max a) Source

Traversable Min Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) Source

sequenceA :: Applicative f => Min (f a) -> f (Min a) Source

mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) Source

sequence :: Monad m => Min (m a) -> m (Min a) Source

Traversable NonEmpty Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) Source

sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) Source

mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) Source

sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) Source

Traversable Identity Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) Source

sequenceA :: Applicative f => Identity (f a) -> f (Identity a) Source

mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) Source

sequence :: Monad m => Identity (m a) -> m (Identity a) Source

Traversable First Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source

sequenceA :: Applicative f => First (f a) -> f (First a) Source

mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source

sequence :: Monad m => First (m a) -> m (First a) Source

Traversable Last Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source

sequenceA :: Applicative f => Last (f a) -> f (Last a) Source

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source

sequence :: Monad m => Last (m a) -> m (Last a) Source

Traversable Down Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Down a -> f (Down b) Source

sequenceA :: Applicative f => Down (f a) -> f (Down a) Source

mapM :: Monad m => (a -> m b) -> Down a -> m (Down b) Source

sequence :: Monad m => Down (m a) -> m (Down a) Source

Traversable Dual Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) Source

sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source

mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) Source

sequence :: Monad m => Dual (m a) -> m (Dual a) Source

Traversable Product Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) Source

sequenceA :: Applicative f => Product (f a) -> f (Product a) Source

mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) Source

sequence :: Monad m => Product (m a) -> m (Product a) Source

Traversable Sum Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) Source

sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source

mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) Source

sequence :: Monad m => Sum (m a) -> m (Sum a) Source

Traversable ZipList Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) Source

sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) Source

mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) Source

sequence :: Monad m => ZipList (m a) -> m (ZipList a) Source

Traversable Par1 Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) Source

sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) Source

mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) Source

sequence :: Monad m => Par1 (m a) -> m (Par1 a) Source

Traversable TyVarBndr Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

traverse :: Applicative f => (a -> f b) -> TyVarBndr a -> f (TyVarBndr b) Source

sequenceA :: Applicative f => TyVarBndr (f a) -> f (TyVarBndr a) Source

mapM :: Monad m => (a -> m b) -> TyVarBndr a -> m (TyVarBndr b) Source

sequence :: Monad m => TyVarBndr (m a) -> m (TyVarBndr a) Source

Traversable Maybe Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) Source

sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) Source

mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) Source

sequence :: Monad m => Maybe (m a) -> m (Maybe a) Source

Traversable Solo Source

Since: base-4.15

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Solo a -> f (Solo b) Source

sequenceA :: Applicative f => Solo (f a) -> f (Solo a) Source

mapM :: Monad m => (a -> m b) -> Solo a -> m (Solo b) Source

sequence :: Monad m => Solo (m a) -> m (Solo a) Source

Traversable [] Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> [a] -> f [b] Source

sequenceA :: Applicative f => [f a] -> f [a] Source

mapM :: Monad m => (a -> m b) -> [a] -> m [b] Source

sequence :: Monad m => [m a] -> m [a] Source

Traversable (Arg a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) Source

sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) Source

mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) Source

sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) Source

Ix i => Traversable (Array i) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) Source

sequenceA :: Applicative f => Array i (f a) -> f (Array i a) Source

mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) Source

sequence :: Monad m => Array i (m a) -> m (Array i a) Source

Traversable (Either a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) Source

sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) Source

mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) Source

sequence :: Monad m => Either a (m a0) -> m (Either a a0) Source

Traversable (Proxy :: Type -> Type) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) Source

sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) Source

mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) Source

sequence :: Monad m => Proxy (m a) -> m (Proxy a) Source

Traversable (U1 :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) Source

sequenceA :: Applicative f => U1 (f a) -> f (U1 a) Source

mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) Source

sequence :: Monad m => U1 (m a) -> m (U1 a) Source

Traversable (UAddr :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UAddr a -> f (UAddr b) Source

sequenceA :: Applicative f => UAddr (f a) -> f (UAddr a) Source

mapM :: Monad m => (a -> m b) -> UAddr a -> m (UAddr b) Source

sequence :: Monad m => UAddr (m a) -> m (UAddr a) Source

Traversable (UChar :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UChar a -> f (UChar b) Source

sequenceA :: Applicative f => UChar (f a) -> f (UChar a) Source

mapM :: Monad m => (a -> m b) -> UChar a -> m (UChar b) Source

sequence :: Monad m => UChar (m a) -> m (UChar a) Source

Traversable (UDouble :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b) Source

sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a) Source

mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b) Source

sequence :: Monad m => UDouble (m a) -> m (UDouble a) Source

Traversable (UFloat :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UFloat a -> f (UFloat b) Source

sequenceA :: Applicative f => UFloat (f a) -> f (UFloat a) Source

mapM :: Monad m => (a -> m b) -> UFloat a -> m (UFloat b) Source

sequence :: Monad m => UFloat (m a) -> m (UFloat a) Source

Traversable (UInt :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UInt a -> f (UInt b) Source

sequenceA :: Applicative f => UInt (f a) -> f (UInt a) Source

mapM :: Monad m => (a -> m b) -> UInt a -> m (UInt b) Source

sequence :: Monad m => UInt (m a) -> m (UInt a) Source

Traversable (UWord :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UWord a -> f (UWord b) Source

sequenceA :: Applicative f => UWord (f a) -> f (UWord a) Source

mapM :: Monad m => (a -> m b) -> UWord a -> m (UWord b) Source

sequence :: Monad m => UWord (m a) -> m (UWord a) Source

Traversable (V1 :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) Source

sequenceA :: Applicative f => V1 (f a) -> f (V1 a) Source

mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) Source

sequence :: Monad m => V1 (m a) -> m (V1 a) Source

Traversable ((,) a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a0 -> f b) -> (a, a0) -> f (a, b) Source

sequenceA :: Applicative f => (a, f a0) -> f (a, a0) Source

mapM :: Monad m => (a0 -> m b) -> (a, a0) -> m (a, b) Source

sequence :: Monad m => (a, m a0) -> m (a, a0) Source

Traversable (Const m :: Type -> Type) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) Source

sequenceA :: Applicative f => Const m (f a) -> f (Const m a) Source

mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) Source

sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) Source

Traversable f => Traversable (Ap f) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) Source

sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) Source

mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) Source

sequence :: Monad m => Ap f (m a) -> m (Ap f a) Source

Traversable f => Traversable (Alt f) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) Source

sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) Source

mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) Source

sequence :: Monad m => Alt f (m a) -> m (Alt f a) Source

Traversable f => Traversable (Rec1 f) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) Source

sequenceA :: Applicative f0 => Rec1 f (f0 a) -> f0 (Rec1 f a) Source

mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b) Source

sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a) Source

(Traversable f, Traversable g) => Traversable (Product f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) Source

sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) Source

mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) Source

sequence :: Monad m => Product f g (m a) -> m (Product f g a) Source

(Traversable f, Traversable g) => Traversable (Sum f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) Source

sequenceA :: Applicative f0 => Sum f g (f0 a) -> f0 (Sum f g a) Source

mapM :: Monad m => (a -> m b) -> Sum f g a -> m (Sum f g b) Source

sequence :: Monad m => Sum f g (m a) -> m (Sum f g a) Source

(Traversable f, Traversable g) => Traversable (f :*: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> (f :*: g) a -> f0 ((f :*: g) b) Source

sequenceA :: Applicative f0 => (f :*: g) (f0 a) -> f0 ((f :*: g) a) Source

mapM :: Monad m => (a -> m b) -> (f :*: g) a -> m ((f :*: g) b) Source

sequence :: Monad m => (f :*: g) (m a) -> m ((f :*: g) a) Source

(Traversable f, Traversable g) => Traversable (f :+: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) Source

sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) Source

mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) Source

sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) Source

Traversable (K1 i c :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b) Source

sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a) Source

mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b) Source

sequence :: Monad m => K1 i c (m a) -> m (K1 i c a) Source

(Traversable f, Traversable g) => Traversable (Compose f g) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) Source

sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a) Source

mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b) Source

sequence :: Monad m => Compose f g (m a) -> m (Compose f g a) Source

(Traversable f, Traversable g) => Traversable (f :.: g) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) Source

sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) Source

mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) Source

sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) Source

Traversable f => Traversable (M1 i c f) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) Source

sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a) Source

mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) Source

sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) Source

Miscellaneous functions

id :: a -> a Source

Identity function.

id x = x

This function might seem useless at first glance, but it can be very useful in a higher order context.

Examples
Expand
>>> length $ filter id [True, True, False, True]
3
>>> Just (Just 3) >>= id
Just 3
>>> foldr id 0 [(^3), (*5), (+2)]
1000

const :: a -> b -> a Source

const x y always evaluates to x, ignoring its second argument.

const x = \_ -> x

This function might seem useless at first glance, but it can be very useful in a higher order context.

Examples
Expand
>>> const 42 "hello"
42
>>> map (const 42) [0..3]
[42,42,42,42]

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9 Source

Right to left function composition.

(f . g) x = f (g x)
f . id = f = id . f
Examples
Expand
>>> map ((*2) . length) [[], [0, 1, 2], [0]]
[0,6,2]
>>> foldr (.) id [(+1), (*3), (^3)] 2
25
>>> let (...) = (.).(.) in ((*2)...(+)) 5 10
30

flip :: (a -> b -> c) -> b -> a -> c Source

flip f takes its (first) two arguments in the reverse order of f.

flip f x y = f y x
flip . flip = id
Examples
Expand
>>> flip (++) "hello" "world"
"worldhello"
>>> let (.>) = flip (.) in (+1) .> show $ 5
"6"

($) :: (a -> b) -> a -> b infixr 0 Source

($) is the function application operator.

Applying ($) to a function f and an argument x gives the same result as applying f to x directly. The definition is akin to this:

($) :: (a -> b) -> a -> b
($) f x = f x

This is id specialized from a -> a to (a -> b) -> (a -> b) which by the associativity of (->) is the same as (a -> b) -> a -> b.

On the face of it, this may appear pointless! But it's actually one of the most useful and important operators in Haskell.

The order of operations is very different between ($) and normal function application. Normal function application has precedence 10 - higher than any operator - and associates to the left. So these two definitions are equivalent:

expr = min 5 1 + 5
expr = ((min 5) 1) + 5

($) has precedence 0 (the lowest) and associates to the right, so these are equivalent:

expr = min 5 $ 1 + 5
expr = (min 5) (1 + 5)
Examples
Expand

A common use cases of ($) is to avoid parentheses in complex expressions.

For example, instead of using nested parentheses in the following Haskell function:

-- | Sum numbers in a string: strSum "100  5 -7" == 98
strSum :: String -> Int
strSum s = sum (mapMaybe readMaybe (words s))

we can deploy the function application operator:

-- | Sum numbers in a string: strSum "100  5 -7" == 98
strSum :: String -> Int
strSum s = sum $ mapMaybe readMaybe $ words s

($) is also used as a section (a partially applied operator), in order to indicate that we wish to apply some yet-unspecified function to a given value. For example, to apply the argument 5 to a list of functions:

applyFive :: [Int]
applyFive = map ($ 5) [(+1), (2^)]
>>> [6, 32]
Technical Remark (Representation Polymorphism)
Expand

($) is fully representation-polymorphic. This allows it to also be used with arguments of unlifted and even unboxed kinds, such as unboxed integers:

fastMod :: Int -> Int -> Int
fastMod (I# x) (I# m) = I# $ remInt# x m

until :: (a -> Bool) -> (a -> a) -> a -> a Source

until p f yields the result of applying f until p holds.

asTypeOf :: a -> a -> a Source

asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

error :: HasCallStack => [Char] -> a Source

error stops execution and displays an error message.

errorWithoutStackTrace :: [Char] -> a Source

A variant of error that does not produce a stack trace.

Since: base-4.9.0.0

undefined :: HasCallStack => a Source

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

seq :: a -> b -> b infixr 0 Source

The value of seq a b is bottom if a is bottom, and otherwise equal to b. In other words, it evaluates the first argument a to weak head normal form (WHNF). seq is usually introduced to improve performance by avoiding unneeded laziness.

A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.

($!) :: (a -> b) -> a -> b infixr 0 Source

Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.

List operations

map :: (a -> b) -> [a] -> [b] Source

\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to each element of xs, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
map f [x1, x2, ...] == [f x1, f x2, ...]

this means that map id == id

Examples
Expand
>>> map (+1) [1, 2, 3]
[2,3,4]
>>> map id [1, 2, 3]
[1,2,3]
>>> map (\n -> 3 * n + 1) [1, 2, 3]
[4,7,10]

(++) :: [a] -> [a] -> [a] infixr 5 Source

(++) appends two lists, i.e.,

[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
[x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

Performance considerations
Expand

This function takes linear time in the number of elements of the first list. Thus it is better to associate repeated applications of (++) to the right (which is the default behaviour): xs ++ (ys ++ zs) or simply xs ++ ys ++ zs, but not (xs ++ ys) ++ zs. For the same reason concat = foldr (++) [] has linear performance, while foldl (++) [] is prone to quadratic slowdown

Examples
Expand
>>> [1, 2, 3] ++ [4, 5, 6]
[1,2,3,4,5,6]
>>> [] ++ [1, 2, 3]
[1,2,3]
>>> [3, 2, 1] ++ []
[3,2,1]

filter :: (a -> Bool) -> [a] -> [a] Source

\(\mathcal{O}(n)\). filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

filter p xs = [ x | x <- xs, p x]
Examples
Expand
>>> filter odd [1, 2, 3]
[1,3]
>>> filter (\l -> length l > 3) ["Hello", ", ", "World", "!"]
["Hello","World"]
>>> filter (/= 3) [1, 2, 3, 4, 3, 2, 1]
[1,2,4,2,1]

head :: HasCallStack => [a] -> a Source

Warning: This is a partial function, it throws an error on empty lists. Use pattern matching, uncons or listToMaybe instead. Consider refactoring to use Data.List.NonEmpty.

\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.

To disable the warning about partiality put {-# OPTIONS_GHC -Wno-x-partial -Wno-unrecognised-warning-flags #-} at the top of the file. To disable it throughout a package put the same options into ghc-options section of Cabal file. To disable it in GHCi put :set -Wno-x-partial -Wno-unrecognised-warning-flags into ~/.ghci config file. See also the migration guide.

Examples
Expand
>>> head [1, 2, 3]
1
>>> head [1..]
1
>>> head []
*** Exception: Prelude.head: empty list

last :: HasCallStack => [a] -> a Source

\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.

WARNING: This function is partial. Consider using unsnoc instead.

Examples
Expand
>>> last [1, 2, 3]
3
>>> last [1..]
* Hangs forever *
>>> last []
*** Exception: Prelude.last: empty list

tail :: HasCallStack => [a] -> [a] Source

Warning: This is a partial function, it throws an error on empty lists. Replace it with drop 1, or use pattern matching or uncons instead. Consider refactoring to use Data.List.NonEmpty.

\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.

To disable the warning about partiality put {-# OPTIONS_GHC -Wno-x-partial -Wno-unrecognised-warning-flags #-} at the top of the file. To disable it throughout a package put the same options into ghc-options section of Cabal file. To disable it in GHCi put :set -Wno-x-partial -Wno-unrecognised-warning-flags into ~/.ghci config file. See also the migration guide.

Examples
Expand
>>> tail [1, 2, 3]
[2,3]
>>> tail [1]
[]
>>> tail []
*** Exception: Prelude.tail: empty list

init :: HasCallStack => [a] -> [a] Source

\(\mathcal{O}(n)\). Return all the elements of a list except the last one. The list must be non-empty.

WARNING: This function is partial. Consider using unsnoc instead.

Examples
Expand
>>> init [1, 2, 3]
[1,2]
>>> init [1]
[]
>>> init []
*** Exception: Prelude.init: empty list

(!!) :: HasCallStack => [a] -> Int -> a infixl 9 Source

List index (subscript) operator, starting from 0. It is an instance of the more general genericIndex, which takes an index of any integral type.

WARNING: This function is partial, and should only be used if you are sure that the indexing will not fail. Otherwise, use !?.

WARNING: This function takes linear time in the index.

Examples
Expand
>>> ['a', 'b', 'c'] !! 0
'a'
>>> ['a', 'b', 'c'] !! 2
'c'
>>> ['a', 'b', 'c'] !! 3
*** Exception: Prelude.!!: index too large
>>> ['a', 'b', 'c'] !! (-1)
*** Exception: Prelude.!!: negative index

null :: Foldable t => t a -> Bool Source

Test whether the structure is empty. The default implementation is Left-associative and lazy in both the initial element and the accumulator. Thus optimised for structures where the first element can be accessed in constant time. Structures where this is not the case should have a non-default implementation.

Examples
Expand

Basic usage:

>>> null []
True
>>> null [1]
False

null is expected to terminate even for infinite structures. The default implementation terminates provided the structure is bounded on the left (there is a leftmost element).

>>> null [1..]
False

Since: base-4.8.0.0

length :: Foldable t => t a -> Int Source

Returns the size/length of a finite structure as an Int. The default implementation just counts elements starting with the leftmost. Instances for structures that can compute the element count faster than via element-by-element counting, should provide a specialised implementation.

Examples
Expand

Basic usage:

>>> length []
0
>>> length ['a', 'b', 'c']
3
>>> length [1..]
* Hangs forever *

Since: base-4.8.0.0

reverse :: [a] -> [a] Source

\(\mathcal{O}(n)\). reverse xs returns the elements of xs in reverse order. xs must be finite.

Laziness
Expand

reverse is lazy in its elements.

>>> head (reverse [undefined, 1])
1
>>> reverse (1 : 2 : undefined)
*** Exception: Prelude.undefined
Examples
Expand
>>> reverse []
[]
>>> reverse [42]
[42]
>>> reverse [2,5,7]
[7,5,2]
>>> reverse [1..]
* Hangs forever *

Special folds

and :: Foldable t => t Bool -> Bool Source

and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

Examples
Expand

Basic usage:

>>> and []
True
>>> and [True]
True
>>> and [False]
False
>>> and [True, True, False]
False
>>> and (False : repeat True) -- Infinite list [False,True,True,True,...
False
>>> and (repeat True)
* Hangs forever *

or :: Foldable t => t Bool -> Bool Source

or returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

Examples
Expand

Basic usage:

>>> or []
False
>>> or [True]
True
>>> or [False]
False
>>> or [True, True, False]
True
>>> or (True : repeat False) -- Infinite list [True,False,False,False,...
True
>>> or (repeat False)
* Hangs forever *

any :: Foldable t => (a -> Bool) -> t a -> Bool Source

Determines whether any element of the structure satisfies the predicate.

Examples
Expand

Basic usage:

>>> any (> 3) []
False
>>> any (> 3) [1,2]
False
>>> any (> 3) [1,2,3,4,5]
True
>>> any (> 3) [1..]
True
>>> any (> 3) [0, -1..]
* Hangs forever *

all :: Foldable t => (a -> Bool) -> t a -> Bool Source

Determines whether all elements of the structure satisfy the predicate.

Examples
Expand

Basic usage:

>>> all (> 3) []
True
>>> all (> 3) [1,2]
False
>>> all (> 3) [1,2,3,4,5]
False
>>> all (> 3) [1..]
False
>>> all (> 3) [4..]
* Hangs forever *

concat :: Foldable t => t [a] -> [a] Source

The concatenation of all the elements of a container of lists.

Examples
Expand

Basic usage:

>>> concat (Just [1, 2, 3])
[1,2,3]
>>> concat (Left 42)
[]
>>> concat [[1, 2, 3], [4, 5], [6], []]
[1,2,3,4,5,6]

concatMap :: Foldable t => (a -> [b]) -> t a -> [b] Source

Map a function over all the elements of a container and concatenate the resulting lists.

Examples
Expand

Basic usage:

>>> concatMap (take 3) [[1..], [10..], [100..], [1000..]]
[1,2,3,10,11,12,100,101,102,1000,1001,1002]
>>> concatMap (take 3) (Just [1..])
[1,2,3]

Building lists

Scans

scanl :: (b -> a -> b) -> b -> [a] -> [b] Source

\(\mathcal{O}(n)\). scanl is similar to foldl, but returns a list of successive reduced values from the left:

scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

Note that

last (scanl f z xs) == foldl f z xs
Examples
Expand
>>> scanl (+) 0 [1..4]
[0,1,3,6,10]
>>> scanl (+) 42 []
[42]
>>> scanl (-) 100 [1..4]
[100,99,97,94,90]
>>> scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
["foo","afoo","bafoo","cbafoo","dcbafoo"]
>>> take 10 (scanl (+) 0 [1..])
[0,1,3,6,10,15,21,28,36,45]
>>> take 1 (scanl undefined 'a' undefined)
"a"

scanl1 :: (a -> a -> a) -> [a] -> [a] Source

\(\mathcal{O}(n)\). scanl1 is a variant of scanl that has no starting value argument:

scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
Examples
Expand
>>> scanl1 (+) [1..4]
[1,3,6,10]
>>> scanl1 (+) []
[]
>>> scanl1 (-) [1..4]
[1,-1,-4,-8]
>>> scanl1 (&&) [True, False, True, True]
[True,False,False,False]
>>> scanl1 (||) [False, False, True, True]
[False,False,True,True]
>>> take 10 (scanl1 (+) [1..])
[1,3,6,10,15,21,28,36,45,55]
>>> take 1 (scanl1 undefined ('a' : undefined))
"a"

scanr :: (a -> b -> b) -> b -> [a] -> [b] Source

\(\mathcal{O}(n)\). scanr is the right-to-left dual of scanl. Note that the order of parameters on the accumulating function are reversed compared to scanl. Also note that

head (scanr f z xs) == foldr f z xs.
Examples
Expand
>>> scanr (+) 0 [1..4]
[10,9,7,4,0]
>>> scanr (+) 42 []
[42]
>>> scanr (-) 100 [1..4]
[98,-97,99,-96,100]
>>> scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]
>>> force $ scanr (+) 0 [1..]
*** Exception: stack overflow

scanr1 :: (a -> a -> a) -> [a] -> [a] Source

\(\mathcal{O}(n)\). scanr1 is a variant of scanr that has no starting value argument.

Examples
Expand
>>> scanr1 (+) [1..4]
[10,9,7,4]
>>> scanr1 (+) []
[]
>>> scanr1 (-) [1..4]
[-2,3,-1,4]
>>> scanr1 (&&) [True, False, True, True]
[False,False,True,True]
>>> scanr1 (||) [True, True, False, False]
[True,True,False,False]
>>> force $ scanr1 (+) [1..]
*** Exception: stack overflow

Infinite lists

iterate :: (a -> a) -> a -> [a] Source

iterate f x returns an infinite list of repeated applications of f to x:

iterate f x == [x, f x, f (f x), ...]
Laziness
Expand

Note that iterate is lazy, potentially leading to thunk build-up if the consumer doesn't force each iterate. See iterate' for a strict variant of this function.

>>> take 1 $ iterate undefined 42
[42]
Examples
Expand
>>> take 10 $ iterate not True
[True,False,True,False,True,False,True,False,True,False]
>>> take 10 $ iterate (+3) 42
[42,45,48,51,54,57,60,63,66,69]

iterate id == repeat:

>>> take 10 $ iterate id 1
[1,1,1,1,1,1,1,1,1,1]

repeat :: a -> [a] Source

repeat x is an infinite list, with x the value of every element.

Examples
Expand
>>> take 10 $ repeat 17
[17,17,17,17,17,17,17,17,17, 17]
>>> repeat undefined
[*** Exception: Prelude.undefined

replicate :: Int -> a -> [a] Source

replicate n x is a list of length n with x the value of every element. It is an instance of the more general genericReplicate, in which n may be of any integral type.

Examples
Expand
>>> replicate 0 True
[]
>>> replicate (-1) True
[]
>>> replicate 4 True
[True,True,True,True]

cycle :: HasCallStack => [a] -> [a] Source

cycle ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.

Examples
Expand
>>> cycle []
*** Exception: Prelude.cycle: empty list
>>> take 10 (cycle [42])
[42,42,42,42,42,42,42,42,42,42]
>>> take 10 (cycle [2, 5, 7])
[2,5,7,2,5,7,2,5,7,2]
>>> take 1 (cycle (42 : undefined))
[42]

Sublists

take :: Int -> [a] -> [a] Source

take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n >= length xs.

It is an instance of the more general genericTake, in which n may be of any integral type.

Laziness
Expand
>>> take 0 undefined
[]
>>> take 2 (1 : 2 : undefined)
[1,2]
Examples
Expand
>>> take 5 "Hello World!"
"Hello"
>>> take 3 [1,2,3,4,5]
[1,2,3]
>>> take 3 [1,2]
[1,2]
>>> take 3 []
[]
>>> take (-1) [1,2]
[]
>>> take 0 [1,2]
[]

drop :: Int -> [a] -> [a] Source

drop n xs returns the suffix of xs after the first n elements, or [] if n >= length xs.

It is an instance of the more general genericDrop, in which n may be of any integral type.

Examples
Expand
>>> drop 6 "Hello World!"
"World!"
>>> drop 3 [1,2,3,4,5]
[4,5]
>>> drop 3 [1,2]
[]
>>> drop 3 []
[]
>>> drop (-1) [1,2]
[1,2]
>>> drop 0 [1,2]
[1,2]

takeWhile :: (a -> Bool) -> [a] -> [a] Source

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p.

Laziness
Expand
>>> takeWhile (const False) undefined
*** Exception: Prelude.undefined
>>> takeWhile (const False) (undefined : undefined)
[]
>>> take 1 (takeWhile (const True) (1 : undefined))
[1]
Examples
Expand
>>> takeWhile (< 3) [1,2,3,4,1,2,3,4]
[1,2]
>>> takeWhile (< 9) [1,2,3]
[1,2,3]
>>> takeWhile (< 0) [1,2,3]
[]

dropWhile :: (a -> Bool) -> [a] -> [a] Source

dropWhile p xs returns the suffix remaining after takeWhile p xs.

Examples
Expand
>>> dropWhile (< 3) [1,2,3,4,5,1,2,3]
[3,4,5,1,2,3]
>>> dropWhile (< 9) [1,2,3]
[]
>>> dropWhile (< 0) [1,2,3]
[1,2,3]

span :: (a -> Bool) -> [a] -> ([a], [a]) Source

span, applied to a predicate p and a list xs, returns a tuple where first element is the longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:

span p xs is equivalent to (takeWhile p xs, dropWhile p xs), even if p is _|_.

Laziness
Expand
>>> span undefined []
([],[])
>>> fst (span (const False) undefined)
*** Exception: Prelude.undefined
>>> fst (span (const False) (undefined : undefined))
[]
>>> take 1 (fst (span (const True) (1 : undefined)))
[1]

span produces the first component of the tuple lazily:

>>> take 10 (fst (span (const True) [1..]))
[1,2,3,4,5,6,7,8,9,10]
Examples
Expand
>>> span (< 3) [1,2,3,4,1,2,3,4]
([1,2],[3,4,1,2,3,4])
>>> span (< 9) [1,2,3]
([1,2,3],[])
>>> span (< 0) [1,2,3]
([],[1,2,3])

break :: (a -> Bool) -> [a] -> ([a], [a]) Source

break, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that do not satisfy p and second element is the remainder of the list:

break p is equivalent to span (not . p) and consequently to (takeWhile (not . p) xs, dropWhile (not . p) xs), even if p is _|_.

Laziness
Expand
>>> break undefined []
([],[])
>>> fst (break (const True) undefined)
*** Exception: Prelude.undefined
>>> fst (break (const True) (undefined : undefined))
[]
>>> take 1 (fst (break (const False) (1 : undefined)))
[1]

break produces the first component of the tuple lazily:

>>> take 10 (fst (break (const False) [1..]))
[1,2,3,4,5,6,7,8,9,10]
Examples
Expand
>>> break (> 3) [1,2,3,4,1,2,3,4]
([1,2,3],[4,1,2,3,4])
>>> break (< 9) [1,2,3]
([],[1,2,3])
>>> break (> 9) [1,2,3]
([1,2,3],[])

splitAt :: Int -> [a] -> ([a], [a]) Source

splitAt n xs returns a tuple where first element is xs prefix of length n and second element is the remainder of the list:

splitAt is an instance of the more general genericSplitAt, in which n may be of any integral type.

Laziness
Expand

It is equivalent to (take n xs, drop n xs) unless n is _|_: splitAt _|_ xs = _|_, not (_|_, _|_)).

The first component of the tuple is produced lazily:

>>> fst (splitAt 0 undefined)
[]
>>> take 1 (fst (splitAt 10 (1 : undefined)))
[1]
Examples
Expand
>>> splitAt 6 "Hello World!"
("Hello ","World!")
>>> splitAt 3 [1,2,3,4,5]
([1,2,3],[4,5])
>>> splitAt 1 [1,2,3]
([1],[2,3])
>>> splitAt 3 [1,2,3]
([1,2,3],[])
>>> splitAt 4 [1,2,3]
([1,2,3],[])
>>> splitAt 0 [1,2,3]
([],[1,2,3])
>>> splitAt (-1) [1,2,3]
([],[1,2,3])

Searching lists

notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 Source

notElem is the negation of elem.

Examples
Expand

Basic usage:

>>> 3 `notElem` []
True
>>> 3 `notElem` [1,2]
True
>>> 3 `notElem` [1,2,3,4,5]
False

For infinite structures, notElem terminates if the value exists at a finite distance from the left side of the structure:

>>> 3 `notElem` [1..]
False
>>> 3 `notElem` ([4..] ++ [3])
* Hangs forever *

lookup :: Eq a => a -> [(a, b)] -> Maybe b Source

\(\mathcal{O}(n)\). lookup key assocs looks up a key in an association list. For the result to be Nothing, the list must be finite.

Examples
Expand
>>> lookup 2 []
Nothing
>>> lookup 2 [(1, "first")]
Nothing
>>> lookup 2 [(1, "first"), (2, "second"), (3, "third")]
Just "second"

Zipping and unzipping lists

zip :: [a] -> [b] -> [(a, b)] Source

\(\mathcal{O}(\min(m,n))\). zip takes two lists and returns a list of corresponding pairs.

zip is right-lazy:

>>> zip [] undefined
[]
>>> zip undefined []
*** Exception: Prelude.undefined
...

zip is capable of list fusion, but it is restricted to its first list argument and its resulting list.

Examples
Expand
>>> zip [1, 2, 3] ['a', 'b', 'c']
[(1,'a'),(2,'b'),(3,'c')]

If one input list is shorter than the other, excess elements of the longer list are discarded, even if one of the lists is infinite:

>>> zip [1] ['a', 'b']
[(1,'a')]
>>> zip [1, 2] ['a']
[(1,'a')]
>>> zip [] [1..]
[]
>>> zip [1..] []
[]

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)] Source

zip3 takes three lists and returns a list of triples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] Source

\(\mathcal{O}(\min(m,n))\). zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function.

zipWith (,) xs ys == zip xs ys
zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]

zipWith is right-lazy:

>>> let f = undefined
>>> zipWith f [] undefined
[]

zipWith is capable of list fusion, but it is restricted to its first list argument and its resulting list.

Examples
Expand

zipWith (+) can be applied to two lists to produce the list of corresponding sums:

>>> zipWith (+) [1, 2, 3] [4, 5, 6]
[5,7,9]
>>> zipWith (++) ["hello ", "foo"] ["world!", "bar"]
["hello world!","foobar"]

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] Source

\(\mathcal{O}(\min(l,m,n))\). The zipWith3 function takes a function which combines three elements, as well as three lists and returns a list of the function applied to corresponding elements, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zipWith3 (,,) xs ys zs == zip3 xs ys zs
zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
Examples
Expand
>>> zipWith3 (\x y z -> [x, y, z]) "123" "abc" "xyz"
["1ax","2by","3cz"]
>>> zipWith3 (\x y z -> (x * y) + z) [1, 2, 3] [4, 5, 6] [7, 8, 9]
[11,18,27]

unzip :: [(a, b)] -> ([a], [b]) Source

unzip transforms a list of pairs into a list of first components and a list of second components.

Examples
Expand
>>> unzip []
([],[])
>>> unzip [(1, 'a'), (2, 'b')]
([1,2],"ab")

unzip3 :: [(a, b, c)] -> ([a], [b], [c]) Source

The unzip3 function takes a list of triples and returns three lists of the respective components, analogous to unzip.

Examples
Expand
>>> unzip3 []
([],[],[])
>>> unzip3 [(1, 'a', True), (2, 'b', False)]
([1,2],"ab",[True,False])

Functions on strings

lines :: String -> [String] Source

Splits the argument into a list of lines stripped of their terminating \n characters. The \n terminator is optional in a final non-empty line of the argument string.

When the argument string is empty, or ends in a \n character, it can be recovered by passing the result of lines to the unlines function. Otherwise, unlines appends the missing terminating \n. This makes unlines . lines idempotent:

(unlines . lines) . (unlines . lines) = (unlines . lines)
Examples
Expand
>>> lines ""           -- empty input contains no lines
[]
>>> lines "\n"         -- single empty line
[""]
>>> lines "one"        -- single unterminated line
["one"]
>>> lines "one\n"      -- single non-empty line
["one"]
>>> lines "one\n\n"    -- second line is empty
["one",""]
>>> lines "one\ntwo"   -- second line is unterminated
["one","two"]
>>> lines "one\ntwo\n" -- two non-empty lines
["one","two"]

words :: String -> [String] Source

words breaks a string up into a list of words, which were delimited by white space (as defined by isSpace). This function trims any white spaces at the beginning and at the end.

Examples
Expand
>>> words "Lorem ipsum\ndolor"
["Lorem","ipsum","dolor"]
>>> words " foo bar "
["foo","bar"]

unlines :: [String] -> String Source

Appends a \n character to each input string, then concatenates the results. Equivalent to foldMap (s -> s ++ "\n").

Examples
Expand
>>> unlines ["Hello", "World", "!"]
"Hello\nWorld\n!\n"

Note that unlines . lines /= id when the input is not \n-terminated:

>>> unlines . lines $ "foo\nbar"
"foo\nbar\n"

unwords :: [String] -> String Source

unwords joins words with separating spaces (U+0020 SPACE).

unwords is neither left nor right inverse of words:

>>> words (unwords [" "])
[]
>>> unwords (words "foo\nbar")
"foo bar"
Examples
Expand
>>> unwords ["Lorem", "ipsum", "dolor"]
"Lorem ipsum dolor"
>>> unwords ["foo", "bar", "", "baz"]
"foo bar  baz"

Converting to and from String

Converting to String

type ShowS = String -> String Source

The shows functions return a function that prepends the output String to an existing String. This allows constant-time concatenation of results using function composition.

class Show a where Source

Conversion of values to readable Strings.

Derived instances of Show have the following properties, which are compatible with derived instances of Read:

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Show is equivalent to

instance (Show a) => Show (Tree a) where

       showsPrec d (Leaf m) = showParen (d > app_prec) $
            showString "Leaf " . showsPrec (app_prec+1) m
         where app_prec = 10

       showsPrec d (u :^: v) = showParen (d > up_prec) $
            showsPrec (up_prec+1) u .
            showString " :^: "      .
            showsPrec (up_prec+1) v
         where up_prec = 5

Note that right-associativity of :^: is ignored. For example,

Minimal complete definition

showsPrec | show

Methods

showsPrec Source

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> a

the value to be converted to a String

-> ShowS

Convert a value to a readable String.

showsPrec should satisfy the law

showsPrec d x r ++ s  ==  showsPrec d x (r ++ s)

Derived instances of Read and Show satisfy the following:

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

show :: a -> String Source

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

showList :: [a] -> ShowS Source

The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.

Instances
Instances details
Show ByteArray Source

Since: base-4.17.0.0

Instance details

Defined in Data.Array.Byte

Show Timeout Source

Since: base-4.0

Instance details

Defined in System.Timeout

Show Void Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Show

Show ByteOrder Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.ByteOrder

Show ClosureType Source
Instance details

Defined in GHC.Internal.ClosureTypes

Show BlockReason Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Show ThreadId Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Show ThreadStatus Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Show NestedAtomically Source

Since: base-4.0

Instance details

Defined in GHC.Internal.Control.Exception.Base

Show NoMatchingContinuationPrompt Source

Since: base-4.18

Instance details

Defined in GHC.Internal.Control.Exception.Base

Show NoMethodError Source

Since: base-4.0

Instance details

Defined in GHC.Internal.Control.Exception.Base

Show NonTermination Source

Since: base-4.0

Instance details

Defined in GHC.Internal.Control.Exception.Base

Show PatternMatchFail Source

Since: base-4.0

Instance details

Defined in GHC.Internal.Control.Exception.Base

Show RecConError Source

Since: base-4.0

Instance details

Defined in GHC.Internal.Control.Exception.Base

Show RecSelError Source

Since: base-4.0

Instance details

Defined in GHC.Internal.Control.Exception.Base

Show RecUpdError Source

Since: base-4.0

Instance details

Defined in GHC.Internal.Control.Exception.Base

Show TypeError Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Control.Exception.Base

Show Constr Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Show ConstrRep Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Show DataRep Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Show DataType Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Show Fixity Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Show Dynamic Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Dynamic

Show All Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS Source

show :: All -> String Source

showList :: [All] -> ShowS Source

Show Any Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS Source

show :: Any -> String Source

showList :: [Any] -> ShowS Source

Show SomeTypeRep Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Data.Typeable.Internal

Show Version Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Version

Show ControlMessage Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Control

Methods

showsPrec :: Int -> ControlMessage -> ShowS Source

show :: ControlMessage -> String Source

showList :: [ControlMessage] -> ShowS Source

Show Event Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Show EventLifetime Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Methods

showsPrec :: Int -> EventLifetime -> ShowS Source

show :: EventLifetime -> String Source

showList :: [EventLifetime] -> ShowS Source

Show Lifetime Source

Since: base-4.8.1.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Show Timeout Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Methods

showsPrec :: Int -> Timeout -> ShowS Source

show :: Timeout -> String Source

showList :: [Timeout] -> ShowS Source

Show FdKey Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Manager

Show State Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Manager

Methods

showsPrec :: Int -> State -> ShowS Source

show :: State -> String Source

showList :: [State] -> ShowS Source

Show State Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Event.TimerManager

Methods

showsPrec :: Int -> State -> ShowS Source

show :: State -> String Source

showList :: [State] -> ShowS Source

Show Unique Source

Since: base-4.3.1.0

Instance details

Defined in GHC.Internal.Event.Unique

Methods

showsPrec :: Int -> Unique -> ShowS Source

show :: Unique -> String Source

showList :: [Unique] -> ShowS Source

Show ErrorCall Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Exception

Show ArithException Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Exception.Type

Show SomeException Source

Since: ghc-internal-3.0

Instance details

Defined in GHC.Internal.Exception.Type

Show WhileHandling Source
Instance details

Defined in GHC.Internal.Exception.Type

Show Fingerprint Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Fingerprint.Type

Show CBool Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CClock Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CDouble Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CFloat Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CLLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CPtrdiff Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CSChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CSUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CSigAtomic Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CSize Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CTime Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CUChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CUInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CUIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CUIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CULLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CULong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CUShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show CWchar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Show IntPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Show WordPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Show ForeignSrcLang Source
Instance details

Defined in GHC.Internal.ForeignSrcLang

Show Associativity Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

Show DecidedStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Show Fixity Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

Show SourceStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Show SourceUnpackedness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Show MaskingState Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.IO

Show SeekMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Device

Show CodingFailureMode Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.IO.Encoding.Failure

Show CodingProgress Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.IO.Encoding.Types

Show TextEncoding Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.IO.Encoding.Types

Show AllocationLimitExceeded Source

Since: base-4.7.1.0

Instance details

Defined in GHC.Internal.IO.Exception

Show ArrayException Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Show AssertionFailed Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Show AsyncException Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Show BlockedIndefinitelyOnMVar Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Show BlockedIndefinitelyOnSTM Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Show CompactionFailed Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Show Deadlock Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Show ExitCode Source
Instance details

Defined in GHC.Internal.IO.Exception

Show FixIOException Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Show IOErrorType Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Show IOException Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Show SomeAsyncException Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.IO.Exception

Show FD Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.FD

Methods

showsPrec :: Int -> FD -> ShowS Source

show :: FD -> String Source

showList :: [FD] -> ShowS Source

Show HandlePosn Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Handle

Show FileLockingNotSupported Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Lock.Common

Show BufferMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Show Handle Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Show HandleType Source

Since: base-4.1.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Show Newline Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Show NewlineMode Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Show IOMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.IOMode

Show IoSubSystem Source
Instance details

Defined in GHC.Internal.IO.SubSystem

Show IOPortException Source
Instance details

Defined in GHC.Internal.IOPort

Methods

showsPrec :: Int -> IOPortException -> ShowS Source

show :: IOPortException -> String Source

showList :: [IOPortException] -> ShowS Source

Show InfoProv Source
Instance details

Defined in GHC.Internal.InfoProv.Types

Show Int16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Show Int32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Show Int64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Show Int8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Show Extension Source
Instance details

Defined in GHC.Internal.LanguageExtensions

Show CCFlags Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show ConcFlags Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show DebugFlags Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show DoCostCentres Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show DoHeapProfile Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show DoTrace Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show GCFlags Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show GiveGCStats Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show HpcFlags Source

Since: base-4.20.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show IoManagerFlag Source
Instance details

Defined in GHC.Internal.RTS.Flags

Show MiscFlags Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show ParFlags Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show ProfFlags Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show RTSFlags Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show TickyFlags Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show TraceFlags Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.RTS.Flags

Show FractionalExponentBase Source
Instance details

Defined in GHC.Internal.Real

Show StackEntry Source
Instance details

Defined in GHC.Internal.Stack.CloneStack

Show CallStack Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Show

Show SrcLoc Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Show

Show StaticPtrInfo Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.StaticPtr

Show GCDetails Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Stats

Show RTSStats Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Stats

Show CBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CBlkSize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CCc Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

showsPrec :: Int -> CCc -> ShowS Source

show :: CCc -> String Source

showList :: [CCc] -> ShowS Source

Show CClockId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CDev Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CFsBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CFsFilCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CGid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

showsPrec :: Int -> CId -> ShowS Source

show :: CId -> String Source

showList :: [CId] -> ShowS Source

Show CIno Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CKey Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CMode Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CNfds Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CNlink Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show COff Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CPid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CRLim Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CSocklen Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CSpeed Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CSsize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CTcflag Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CTimer Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show CUid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Show Fd Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Methods

showsPrec :: Int -> Fd -> ShowS Source

show :: Fd -> String Source

showList :: [Fd] -> ShowS Source

Show AnnLookup Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show AnnTarget Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Bang Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show BndrVis Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Body Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Bytes Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Callconv Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Clause Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Con Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

showsPrec :: Int -> Con -> ShowS Source

show :: Con -> String Source

showList :: [Con] -> ShowS Source

Show Dec Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

showsPrec :: Int -> Dec -> ShowS Source

show :: Dec -> String Source

showList :: [Dec] -> ShowS Source

Show DecidedStrictness Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show DerivClause Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show DerivStrategy Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show DocLoc Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Exp Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

showsPrec :: Int -> Exp -> ShowS Source

show :: Exp -> String Source

showList :: [Exp] -> ShowS Source

Show FamilyResultSig Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Fixity Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show FixityDirection Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Foreign Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show FunDep Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Guard Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Info Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show InjectivityAnn Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Inline Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Lit Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

showsPrec :: Int -> Lit -> ShowS Source

show :: Lit -> String Source

showList :: [Lit] -> ShowS Source

Show Loc Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

showsPrec :: Int -> Loc -> ShowS Source

show :: Loc -> String Source

showList :: [Loc] -> ShowS Source

Show Match Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show ModName Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Module Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show ModuleInfo Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Name Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show NameFlavour Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show NameSpace Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show NamespaceSpecifier Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show OccName Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Overlap Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Pat Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

showsPrec :: Int -> Pat -> ShowS Source

show :: Pat -> String Source

showList :: [Pat] -> ShowS Source

Show PatSynArgs Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show PatSynDir Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Phases Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show PkgName Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Pragma Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Range Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Role Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show RuleBndr Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show RuleMatch Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Safety Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show SourceStrictness Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show SourceUnpackedness Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Specificity Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Stmt Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show TyLit Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show TySynEqn Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Type Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show TypeFamilyHead Source
Instance details

Defined in GHC.Internal.TH.Syntax

Show Lexeme Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Text.Read.Lex

Show Number Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Text.Read.Lex

Show SomeChar Source
Instance details

Defined in GHC.Internal.TypeLits

Show SomeSymbol Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.TypeLits

Show SomeNat Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.TypeNats

Show GeneralCategory Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Unicode

Show Word16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Show Word32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Show Word64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Show Word8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Word

Show KindRep Source
Instance details

Defined in GHC.Internal.Show

Show Module Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Show

Show Ordering Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Show TrName Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Show

Show TyCon Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Show TypeLitSort Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Show

Show Integer Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Show Natural Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Show

Show () Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> () -> ShowS Source

show :: () -> String Source

showList :: [()] -> ShowS Source

Show Bool Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Show Char Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Show Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> Int -> ShowS Source

show :: Int -> String Source

showList :: [Int] -> ShowS Source

Show Levity Source

Since: base-4.15.0.0

Instance details

Defined in GHC.Internal.Show

Show RuntimeRep Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Show

Show VecCount Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Show

Show VecElem Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Show

Show Word Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Show a => Show (Complex a) Source

Since: base-2.1

Instance details

Defined in Data.Complex

Show a => Show (First a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> First a -> ShowS Source

show :: First a -> String Source

showList :: [First a] -> ShowS Source

Show a => Show (Last a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Last a -> ShowS Source

show :: Last a -> String Source

showList :: [Last a] -> ShowS Source

Show a => Show (Max a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Max a -> ShowS Source

show :: Max a -> String Source

showList :: [Max a] -> ShowS Source

Show a => Show (Min a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Min a -> ShowS Source

show :: Min a -> String Source

showList :: [Min a] -> ShowS Source

Show m => Show (WrappedMonoid m) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show a => Show (NonEmpty a) Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Show

Show a => Show (And a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

showsPrec :: Int -> And a -> ShowS Source

show :: And a -> String Source

showList :: [And a] -> ShowS Source

Show a => Show (Iff a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

showsPrec :: Int -> Iff a -> ShowS Source

show :: Iff a -> String Source

showList :: [Iff a] -> ShowS Source

Show a => Show (Ior a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

showsPrec :: Int -> Ior a -> ShowS Source

show :: Ior a -> String Source

showList :: [Ior a] -> ShowS Source

Show a => Show (Xor a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

showsPrec :: Int -> Xor a -> ShowS Source

show :: Xor a -> String Source

showList :: [Xor a] -> ShowS Source

Show a => Show (Identity a) Source

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Show a => Show (First a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> First a -> ShowS Source

show :: First a -> String Source

showList :: [First a] -> ShowS Source

Show a => Show (Last a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> Last a -> ShowS Source

show :: Last a -> String Source

showList :: [Last a] -> ShowS Source

Show a => Show (Down a) Source

This instance would be equivalent to the derived instances of the Down newtype if the getDown field were removed

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

showsPrec :: Int -> Down a -> ShowS Source

show :: Down a -> String Source

showList :: [Down a] -> ShowS Source

Show a => Show (Dual a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Dual a -> ShowS Source

show :: Dual a -> String Source

showList :: [Dual a] -> ShowS Source

Show a => Show (Product a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Show a => Show (Sum a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS Source

show :: Sum a -> String Source

showList :: [Sum a] -> ShowS Source

Show a => Show (ExceptionWithContext a) Source
Instance details

Defined in GHC.Internal.Exception.Type

Show e => Show (NoBacktrace e) Source
Instance details

Defined in GHC.Internal.Exception.Type

Show (ConstPtr a) Source
Instance details

Defined in GHC.Internal.Foreign.C.ConstPtr

Show (ForeignPtr a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.ForeignPtr

Show a => Show (ZipList a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Show p => Show (Par1 p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> Par1 p -> ShowS Source

show :: Par1 p -> String Source

showList :: [Par1 p] -> ShowS Source

Show (FunPtr a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Ptr

Methods

showsPrec :: Int -> FunPtr a -> ShowS Source

show :: FunPtr a -> String Source

showList :: [FunPtr a] -> ShowS Source

Show (Ptr a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Ptr

Methods

showsPrec :: Int -> Ptr a -> ShowS Source

show :: Ptr a -> String Source

showList :: [Ptr a] -> ShowS Source

Show a => Show (Ratio a) Source

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Real

Methods

showsPrec :: Int -> Ratio a -> ShowS Source

show :: Ratio a -> String Source

showList :: [Ratio a] -> ShowS Source

Show flag => Show (TyVarBndr flag) Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

showsPrec :: Int -> TyVarBndr flag -> ShowS Source

show :: TyVarBndr flag -> String Source

showList :: [TyVarBndr flag] -> ShowS Source

Show (SChar c) Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.TypeLits

Methods

showsPrec :: Int -> SChar c -> ShowS Source

show :: SChar c -> String Source

showList :: [SChar c] -> ShowS Source

Show (SSymbol s) Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.TypeLits

Show (SNat n) Source

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.TypeNats

Methods

showsPrec :: Int -> SNat n -> ShowS Source

show :: SNat n -> String Source

showList :: [SNat n] -> ShowS Source

Show a => Show (Maybe a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> Maybe a -> ShowS Source

show :: Maybe a -> String Source

showList :: [Maybe a] -> ShowS Source

Show a => Show (Solo a) Source

Since: base-4.15

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> Solo a -> ShowS Source

show :: Solo a -> String Source

showList :: [Solo a] -> ShowS Source

Show a => Show [a] Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> [a] -> ShowS Source

show :: [a] -> String Source

showList :: [[a]] -> ShowS Source

HasResolution a => Show (Fixed a) Source

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

showsPrec :: Int -> Fixed a -> ShowS Source

show :: Fixed a -> String Source

showList :: [Fixed a] -> ShowS Source

(Show a, Show b) => Show (Arg a b) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Arg a b -> ShowS Source

show :: Arg a b -> String Source

showList :: [Arg a b] -> ShowS Source

(Ix a, Show a, Show b) => Show (Array a b) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Arr

Methods

showsPrec :: Int -> Array a b -> ShowS Source

show :: Array a b -> String Source

showList :: [Array a b] -> ShowS Source

(Show a, Show b) => Show (Either a b) Source

Since: base-3.0

Instance details

Defined in GHC.Internal.Data.Either

Methods

showsPrec :: Int -> Either a b -> ShowS Source

show :: Either a b -> String Source

showList :: [Either a b] -> ShowS Source

Show (Proxy s) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

showsPrec :: Int -> Proxy s -> ShowS Source

show :: Proxy s -> String Source

showList :: [Proxy s] -> ShowS Source

Show (TypeRep a) Source
Instance details

Defined in GHC.Internal.Data.Typeable.Internal

Show (U1 p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> U1 p -> ShowS Source

show :: U1 p -> String Source

showList :: [U1 p] -> ShowS Source

Show (UAddr p) Source

Since: base-4.21.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> UAddr p -> ShowS Source

show :: UAddr p -> String Source

showList :: [UAddr p] -> ShowS Source

Show (V1 p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> V1 p -> ShowS Source

show :: V1 p -> String Source

showList :: [V1 p] -> ShowS Source

Show (ST s a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.ST

Methods

showsPrec :: Int -> ST s a -> ShowS Source

show :: ST s a -> String Source

showList :: [ST s a] -> ShowS Source

(Show a, Show b) => Show (a, b) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b) -> ShowS Source

show :: (a, b) -> String Source

showList :: [(a, b)] -> ShowS Source

Show (a -> b) Source

Since: base-2.1

Instance details

Defined in Text.Show.Functions

Methods

showsPrec :: Int -> (a -> b) -> ShowS Source

show :: (a -> b) -> String Source

showList :: [a -> b] -> ShowS Source

Show a => Show (Const a b) Source

This instance would be equivalent to the derived instances of the Const newtype if the getConst field were removed

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

showsPrec :: Int -> Const a b -> ShowS Source

show :: Const a b -> String Source

showList :: [Const a b] -> ShowS Source

Show (f a) => Show (Ap f a) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> Ap f a -> ShowS Source

show :: Ap f a -> String Source

showList :: [Ap f a] -> ShowS Source

Show (f a) => Show (Alt f a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Alt f a -> ShowS Source

show :: Alt f a -> String Source

showList :: [Alt f a] -> ShowS Source

Show (Coercion a b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Coercion

Methods

showsPrec :: Int -> Coercion a b -> ShowS Source

show :: Coercion a b -> String Source

showList :: [Coercion a b] -> ShowS Source

Show (a :~: b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

Methods

showsPrec :: Int -> (a :~: b) -> ShowS Source

show :: (a :~: b) -> String Source

showList :: [a :~: b] -> ShowS Source

Show (OrderingI a b) Source
Instance details

Defined in GHC.Internal.Data.Type.Ord

Methods

showsPrec :: Int -> OrderingI a b -> ShowS Source

show :: OrderingI a b -> String Source

showList :: [OrderingI a b] -> ShowS Source

Show (f p) => Show (Rec1 f p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> Rec1 f p -> ShowS Source

show :: Rec1 f p -> String Source

showList :: [Rec1 f p] -> ShowS Source

Show (URec Char p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Show (URec Double p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Show (URec Float p) Source
Instance details

Defined in GHC.Internal.Generics

Show (URec Int p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> URec Int p -> ShowS Source

show :: URec Int p -> String Source

showList :: [URec Int p] -> ShowS Source

Show (URec Word p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

(Show a, Show b, Show c) => Show (a, b, c) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c) -> ShowS Source

show :: (a, b, c) -> String Source

showList :: [(a, b, c)] -> ShowS Source

(Show (f a), Show (g a)) => Show (Product f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Product

Methods

showsPrec :: Int -> Product f g a -> ShowS Source

show :: Product f g a -> String Source

showList :: [Product f g a] -> ShowS Source

(Show (f a), Show (g a)) => Show (Sum f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Sum

Methods

showsPrec :: Int -> Sum f g a -> ShowS Source

show :: Sum f g a -> String Source

showList :: [Sum f g a] -> ShowS Source

Show (a :~~: b) Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

Methods

showsPrec :: Int -> (a :~~: b) -> ShowS Source

show :: (a :~~: b) -> String Source

showList :: [a :~~: b] -> ShowS Source

(Show (f p), Show (g p)) => Show ((f :*: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> (f :*: g) p -> ShowS Source

show :: (f :*: g) p -> String Source

showList :: [(f :*: g) p] -> ShowS Source

(Show (f p), Show (g p)) => Show ((f :+: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> (f :+: g) p -> ShowS Source

show :: (f :+: g) p -> String Source

showList :: [(f :+: g) p] -> ShowS Source

Show c => Show (K1 i c p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> K1 i c p -> ShowS Source

show :: K1 i c p -> String Source

showList :: [K1 i c p] -> ShowS Source

(Show a, Show b, Show c, Show d) => Show (a, b, c, d) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d) -> ShowS Source

show :: (a, b, c, d) -> String Source

showList :: [(a, b, c, d)] -> ShowS Source

Show (f (g a)) => Show (Compose f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Compose

Methods

showsPrec :: Int -> Compose f g a -> ShowS Source

show :: Compose f g a -> String Source

showList :: [Compose f g a] -> ShowS Source

Show (f (g p)) => Show ((f :.: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> (f :.: g) p -> ShowS Source

show :: (f :.: g) p -> String Source

showList :: [(f :.: g) p] -> ShowS Source

Show (f p) => Show (M1 i c f p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> M1 i c f p -> ShowS Source

show :: M1 i c f p -> String Source

showList :: [M1 i c f p] -> ShowS Source

(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d, e) -> ShowS Source

show :: (a, b, c, d, e) -> String Source

showList :: [(a, b, c, d, e)] -> ShowS Source

(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f) -> ShowS Source

show :: (a, b, c, d, e, f) -> String Source

showList :: [(a, b, c, d, e, f)] -> ShowS Source

(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g) -> ShowS Source

show :: (a, b, c, d, e, f, g) -> String Source

showList :: [(a, b, c, d, e, f, g)] -> ShowS Source

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h) -> ShowS Source

show :: (a, b, c, d, e, f, g, h) -> String Source

showList :: [(a, b, c, d, e, f, g, h)] -> ShowS Source

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i) -> ShowS Source

show :: (a, b, c, d, e, f, g, h, i) -> String Source

showList :: [(a, b, c, d, e, f, g, h, i)] -> ShowS Source

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j) -> ShowS Source

show :: (a, b, c, d, e, f, g, h, i, j) -> String Source

showList :: [(a, b, c, d, e, f, g, h, i, j)] -> ShowS Source

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k) -> ShowS Source

show :: (a, b, c, d, e, f, g, h, i, j, k) -> String Source

showList :: [(a, b, c, d, e, f, g, h, i, j, k)] -> ShowS Source

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l) -> ShowS Source

show :: (a, b, c, d, e, f, g, h, i, j, k, l) -> String Source

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l)] -> ShowS Source

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> ShowS Source

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> String Source

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m)] -> ShowS Source

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> ShowS Source

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> String Source

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] -> ShowS Source

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> ShowS Source

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> String Source

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] -> ShowS Source

shows :: Show a => a -> ShowS Source

equivalent to showsPrec with a precedence of 0.

showChar :: Char -> ShowS Source

utility function converting a Char to a show function that simply prepends the character unchanged.

showString :: String -> ShowS Source

utility function converting a String to a show function that simply prepends the string unchanged.

showParen :: Bool -> ShowS -> ShowS Source

utility function that surrounds the inner show function with parentheses when the Bool parameter is True.

Converting from String

type ReadS a = String -> [(a, String)] Source

A parser for a type a, represented as a function that takes a String and returns a list of possible parses as (a,String) pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf ReadP).

class Read a where Source

Parsing of Strings, producing values.

Derived instances of Read make the following assumptions, which derived instances of Show obey:

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Read in Haskell 2010 is equivalent to

instance (Read a) => Read (Tree a) where

        readsPrec d r =  readParen (d > app_prec)
                         (\r -> [(Leaf m,t) |
                                 ("Leaf",s) <- lex r,
                                 (m,t) <- readsPrec (app_prec+1) s]) r

                      ++ readParen (d > up_prec)
                         (\r -> [(u:^:v,w) |
                                 (u,s) <- readsPrec (up_prec+1) r,
                                 (":^:",t) <- lex s,
                                 (v,w) <- readsPrec (up_prec+1) t]) r

          where app_prec = 10
                up_prec = 5

Note that right-associativity of :^: is unused.

The derived instance in GHC is equivalent to

instance (Read a) => Read (Tree a) where

        readPrec = parens $ (prec app_prec $ do
                                 Ident "Leaf" <- lexP
                                 m <- step readPrec
                                 return (Leaf m))

                     +++ (prec up_prec $ do
                                 u <- step readPrec
                                 Symbol ":^:" <- lexP
                                 v <- step readPrec
                                 return (u :^: v))

          where app_prec = 10
                up_prec = 5

        readListPrec = readListPrecDefault

Why do both readsPrec and readPrec exist, and why does GHC opt to implement readPrec in derived Read instances instead of readsPrec? The reason is that readsPrec is based on the ReadS type, and although ReadS is mentioned in the Haskell 2010 Report, it is not a very efficient parser data structure.

readPrec, on the other hand, is based on a much more efficient ReadPrec datatype (a.k.a "new-style parsers"), but its definition relies on the use of the RankNTypes language extension. Therefore, readPrec (and its cousin, readListPrec) are marked as GHC-only. Nevertheless, it is recommended to use readPrec instead of readsPrec whenever possible for the efficiency improvements it brings.

As mentioned above, derived Read instances in GHC will implement readPrec instead of readsPrec. The default implementations of readsPrec (and its cousin, readList) will simply use readPrec under the hood. If you are writing a Read instance by hand, it is recommended to write it like so:

instance Read T where
  readPrec     = ...
  readListPrec = readListPrecDefault

Minimal complete definition

readsPrec | readPrec

Methods

readsPrec Source

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> ReadS a

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of Read and Show satisfy the following:

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

readList :: ReadS [a] Source

The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String are expected to use double quotes, rather than square brackets.

Instances
Instances details
Read Void Source

Reading a Void value is always a parse error, considering Void as a data type with no constructors.

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Read

Read ByteOrder Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.ByteOrder

Read All Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Read Any Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Read Version Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Version

Read CBool Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CClock Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CDouble Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CFloat Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CLLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CPtrdiff Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CSChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CSUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CSigAtomic Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CSize Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CTime Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CUChar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CUInt Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CUIntMax Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CUIntPtr Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CULLong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CULong Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CUSeconds Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CUShort Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read CWchar Source
Instance details

Defined in GHC.Internal.Foreign.C.Types

Read IntPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Read WordPtr Source
Instance details

Defined in GHC.Internal.Foreign.Ptr

Read Associativity Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

Read DecidedStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Read Fixity Source

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Generics

Read SourceStrictness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Read SourceUnpackedness Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Read SeekMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Device

Read ExitCode Source
Instance details

Defined in GHC.Internal.IO.Exception

Read BufferMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Read Newline Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Read NewlineMode Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Internal.IO.Handle.Types

Read IOMode Source

Since: base-4.2.0.0

Instance details

Defined in GHC.Internal.IO.IOMode

Read Int16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Read Int32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Read Int64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Read Int8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Int

Read GCDetails Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Stats

Read RTSStats Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Stats

Read CBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CBlkSize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CCc Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CClockId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CDev Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CFsBlkCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CFsFilCnt Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CGid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CId Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CIno Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CKey Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CMode Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CNfds Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CNlink Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read COff Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CPid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CRLim Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CSocklen Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CSpeed Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CSsize Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CTcflag Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read CUid Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read Fd Source
Instance details

Defined in GHC.Internal.System.Posix.Types

Read Lexeme Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read SomeChar Source
Instance details

Defined in GHC.Internal.TypeLits

Read SomeSymbol Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.TypeLits

Read SomeNat Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.TypeNats

Read GeneralCategory Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Word16 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Word32 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Word64 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Word8 Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Ordering Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Integer Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Natural Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Read

Read () Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Bool Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Char Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Double Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Float Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Int Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read Word Source

Since: base-4.5.0.0

Instance details

Defined in GHC.Internal.Read

Read a => Read (Complex a) Source

Since: base-2.1

Instance details

Defined in Data.Complex

Read a => Read (First a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (Last a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (Max a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (Min a) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read m => Read (WrappedMonoid m) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (NonEmpty a) Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Read

Read a => Read (And a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Read a => Read (Iff a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Read a => Read (Ior a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Read a => Read (Xor a) Source

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Read a => Read (Identity a) Source

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Read a => Read (First a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Read a => Read (Last a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Read a => Read (Down a) Source

This instance would be equivalent to the derived instances of the Down newtype if the getDown field were removed

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Read a => Read (Dual a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Read a => Read (Product a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Read a => Read (Sum a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Read a => Read (ZipList a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Read p => Read (Par1 p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

(Integral a, Read a) => Read (Ratio a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read a => Read (Maybe a) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Read a => Read (Solo a) Source

Since: base-4.15

Instance details

Defined in GHC.Internal.Read

Read a => Read [a] Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

HasResolution a => Read (Fixed a) Source

Since: base-4.3.0.0

Instance details

Defined in Data.Fixed

(Read a, Read b) => Read (Arg a b) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

(Ix a, Read a, Read b) => Read (Array a b) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

(Read a, Read b) => Read (Either a b) Source

Since: base-3.0

Instance details

Defined in GHC.Internal.Data.Either

Read (Proxy t) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Read (U1 p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Read (V1 p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

(Read a, Read b) => Read (a, b) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b) Source

readList :: ReadS [(a, b)] Source

readPrec :: ReadPrec (a, b) Source

readListPrec :: ReadPrec [(a, b)] Source

Read a => Read (Const a b) Source

This instance would be equivalent to the derived instances of the Const newtype if the getConst field were removed

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Read (f a) => Read (Ap f a) Source

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Read (f a) => Read (Alt f a) Source

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Coercible a b => Read (Coercion a b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Coercion

a ~ b => Read (a :~: b) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

Read (f p) => Read (Rec1 f p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

(Read a, Read b, Read c) => Read (a, b, c) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c) Source

readList :: ReadS [(a, b, c)] Source

readPrec :: ReadPrec (a, b, c) Source

readListPrec :: ReadPrec [(a, b, c)] Source

(Read (f a), Read (g a)) => Read (Product f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Product

(Read (f a), Read (g a)) => Read (Sum f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Sum

Methods

readsPrec :: Int -> ReadS (Sum f g a) Source

readList :: ReadS [Sum f g a] Source

readPrec :: ReadPrec (Sum f g a) Source

readListPrec :: ReadPrec [Sum f g a] Source

a ~~ b => Read (a :~~: b) Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Data.Type.Equality

(Read (f p), Read (g p)) => Read ((f :*: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

readsPrec :: Int -> ReadS ((f :*: g) p) Source

readList :: ReadS [(f :*: g) p] Source

readPrec :: ReadPrec ((f :*: g) p) Source

readListPrec :: ReadPrec [(f :*: g) p] Source

(Read (f p), Read (g p)) => Read ((f :+: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

readsPrec :: Int -> ReadS ((f :+: g) p) Source

readList :: ReadS [(f :+: g) p] Source

readPrec :: ReadPrec ((f :+: g) p) Source

readListPrec :: ReadPrec [(f :+: g) p] Source

Read c => Read (K1 i c p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

readsPrec :: Int -> ReadS (K1 i c p) Source

readList :: ReadS [K1 i c p] Source

readPrec :: ReadPrec (K1 i c p) Source

readListPrec :: ReadPrec [K1 i c p] Source

(Read a, Read b, Read c, Read d) => Read (a, b, c, d) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d) Source

readList :: ReadS [(a, b, c, d)] Source

readPrec :: ReadPrec (a, b, c, d) Source

readListPrec :: ReadPrec [(a, b, c, d)] Source

Read (f (g a)) => Read (Compose f g a) Source

Since: base-4.18.0.0

Instance details

Defined in Data.Functor.Compose

Read (f (g p)) => Read ((f :.: g) p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

readsPrec :: Int -> ReadS ((f :.: g) p) Source

readList :: ReadS [(f :.: g) p] Source

readPrec :: ReadPrec ((f :.: g) p) Source

readListPrec :: ReadPrec [(f :.: g) p] Source

Read (f p) => Read (M1 i c f p) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

readsPrec :: Int -> ReadS (M1 i c f p) Source

readList :: ReadS [M1 i c f p] Source

readPrec :: ReadPrec (M1 i c f p) Source

readListPrec :: ReadPrec [M1 i c f p] Source

(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e) Source

readList :: ReadS [(a, b, c, d, e)] Source

readPrec :: ReadPrec (a, b, c, d, e) Source

readListPrec :: ReadPrec [(a, b, c, d, e)] Source

(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f) Source

readList :: ReadS [(a, b, c, d, e, f)] Source

readPrec :: ReadPrec (a, b, c, d, e, f) Source

readListPrec :: ReadPrec [(a, b, c, d, e, f)] Source

(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g) Source

readList :: ReadS [(a, b, c, d, e, f, g)] Source

readPrec :: ReadPrec (a, b, c, d, e, f, g) Source

readListPrec :: ReadPrec [(a, b, c, d, e, f, g)] Source

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h) Source

readList :: ReadS [(a, b, c, d, e, f, g, h)] Source

readPrec :: ReadPrec (a, b, c, d, e, f, g, h) Source

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h)] Source

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i) Source

readList :: ReadS [(a, b, c, d, e, f, g, h, i)] Source

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i) Source

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i)] Source

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j) Source

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j)] Source

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j) Source

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j)] Source

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k) Source

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k)] Source

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k) Source

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k)] Source

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l) Source

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l)] Source

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l) Source

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l)] Source

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m) Source

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m)] Source

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m) Source

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m)] Source

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source

reads :: Read a => ReadS a Source

equivalent to readsPrec with a precedence of 0.

readParen :: Bool -> ReadS a -> ReadS a Source

readParen True p parses what p parses, but surrounded with parentheses.

readParen False p parses what p parses, but optionally surrounded with parentheses.

read :: Read a => String -> a Source

The read function reads input from a string, which must be completely consumed by the input process. read fails with an error if the parse is unsuccessful, and it is therefore discouraged from being used in real applications. Use readMaybe or readEither for safe alternatives.

>>> read "123" :: Int
123
>>> read "hello" :: Int
*** Exception: Prelude.read: no parse

lex :: ReadS String Source

The lex function reads a single lexeme from the input, discarding initial white space, and returning the characters that constitute the lexeme. If the input string contains only white space, lex returns a single successful `lexeme' consisting of the empty string. (Thus lex "" = [("","")].) If there is no legal lexeme at the beginning of the input string, lex fails (i.e. returns []).

This lexer is not completely faithful to the Haskell lexical syntax in the following respects:

Basic Input and output

data IO a Source

A value of type IO a is a computation which, when performed, does some I/O before returning a value of type a.

There is really only one way to "perform" an I/O action: bind it to Main.main in your program. When your program is run, the I/O will be performed. It isn't possible to perform I/O from an arbitrary function, unless that function is itself in the IO monad and called at some point, directly or indirectly, from Main.main.

IO is a monad, so IO actions can be combined using either the do-notation or the >> and >>= operations from the Monad class.

Instances
Instances details
Alternative IO Source

Takes the first non-throwing IO action's result. empty throws an exception.

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

empty :: IO a Source

(<|>) :: IO a -> IO a -> IO a Source

some :: IO a -> IO [a] Source

many :: IO a -> IO [a] Source

Applicative IO Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> IO a Source

(<*>) :: IO (a -> b) -> IO a -> IO b Source

liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source

(*>) :: IO a -> IO b -> IO b Source

(<*) :: IO a -> IO b -> IO a Source

Functor IO Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

fmap :: (a -> b) -> IO a -> IO b Source

(<$) :: a -> IO b -> IO a Source

Monad IO Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b Source

(>>) :: IO a -> IO b -> IO b Source

return :: a -> IO a Source

MonadPlus IO Source

Takes the first non-throwing IO action's result. mzero throws an exception.

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

mzero :: IO a Source

mplus :: IO a -> IO a -> IO a Source

MonadFail IO Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fail

Methods

fail :: String -> IO a Source

MonadFix IO Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Control.Monad.Fix

Methods

mfix :: (a -> IO a) -> IO a Source

MonadIO IO Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Control.Monad.IO.Class

Methods

liftIO :: IO a -> IO a Source

GHCiSandboxIO IO Source

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.GHCi

Methods

ghciStepIO :: IO a -> IO a Source

Quasi IO Source
Instance details

Defined in GHC.Internal.TH.Syntax

Quote IO Source
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

newName :: String -> IO Name Source

a ~ () => HPrintfType (IO a) Source

Since: base-4.7.0.0

Instance details

Defined in Text.Printf

Methods

hspr :: Handle -> String -> [UPrintf] -> IO a

a ~ () => PrintfType (IO a) Source

Since: base-4.7.0.0

Instance details

Defined in Text.Printf

Methods

spr :: String -> [UPrintf] -> IO a

Monoid a => Monoid (IO a) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: IO a Source

mappend :: IO a -> IO a -> IO a Source

mconcat :: [IO a] -> IO a Source

Semigroup a => Semigroup (IO a) Source

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Base

Methods

(<>) :: IO a -> IO a -> IO a Source

sconcat :: NonEmpty (IO a) -> IO a Source

stimes :: Integral b => b -> IO a -> IO a Source

Simple I/O operations

Output functions

putChar :: Char -> IO () Source

Write a character to the standard output device

putChar is implemented as hPutChar stdout.

This operation may fail with the same errors as hPutChar.

Examples
Expand

Note that the following do not put a newline.

>>> putChar 'x'
x
>>> putChar '\0042'
*

putStr :: String -> IO () Source

Write a string to the standard output device

putStr is implemented as hPutStr stdout.

This operation may fail with the same errors, and has the same issues with concurrency, as hPutStr!

Examples
Expand

Note that the following do not put a newline.

>>> putStr "Hello, World!"
Hello, World!
>>> putStr "\0052\0042\0050"
4*2

putStrLn :: String -> IO () Source

The same as putStr, but adds a newline character.

This operation may fail with the same errors, and has the same issues with concurrency, as hPutStr!

print :: Show a => a -> IO () Source

The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline.

print is implemented as putStrLn . show

This operation may fail with the same errors, and has the same issues with concurrency, as hPutStr!

Examples
Expand
>>> print [1, 2, 3]
[1,2,3]

Be careful when using print for outputting strings, as this will invoke show and cause strings to be printed with quotation marks and non-ascii symbols escaped.

>>> print "λ :D"
"\995 :D"

A program to print the first 8 integers and their powers of 2 could be written as:

>>> print [(n, 2^n) | n <- [0..8]]
[(0,1),(1,2),(2,4),(3,8),(4,16),(5,32),(6,64),(7,128),(8,256)]

Input functions

getChar :: IO Char Source

Read a single character from the standard input device.

getChar is implemented as hGetChar stdin.

This operation may fail with the same errors as hGetChar.

Examples
Expand
>>> getChar
a'a'
>>> getChar
>
'\n'

getLine :: IO String Source

Read a line from the standard input device.

getLine is implemented as hGetLine stdin.

This operation may fail with the same errors as hGetLine.

Examples
Expand
>>> getLine
> Hello World!
"Hello World!"
>>> getLine
>
""

getContents :: IO String Source

The getContents operation returns all user input as a single string, which is read lazily as it is needed.

getContents is implemented as hGetContents stdin.

This operation may fail with the same errors as hGetContents.

Examples
Expand
>>> getContents >>= putStr
> aaabbbccc :D
aaabbbccc :D
> I hope you have a great day
I hope you have a great day
> ^D
>>> getContents >>= print . length
> abc
> <3
> def ^D
11

interact :: (String -> String) -> IO () Source

interact f takes the entire input from stdin and applies f to it. The resulting string is written to the stdout device.

Note that this operation is lazy, which allows to produce output even before all input has been consumed.

This operation may fail with the same errors as getContents and putStr.

Examples
Expand
>>> interact (\str -> str ++ str)
> hi :)
hi :)
> ^D
hi :)
>>> interact (const ":D")
:D
>>> interact (show . words)
> hello world!
> I hope you have a great day
> ^D
["hello","world!","I","hope","you","have","a","great","day"]

Files

type FilePath = String Source

File and directory names are values of type String, whose precise meaning is operating system dependent. Files can be opened, yielding a handle which can then be used to operate on the contents of that file.

readFile :: FilePath -> IO String Source

The readFile function reads a file and returns the contents of the file as a string.

The file is read lazily, on demand, as with getContents.

This operation may fail with the same errors as hGetContents and openFile.

Examples
Expand
>>> readFile "~/hello_world"
"Greetings!"
>>> take 5 <$> readFile "/dev/zero"
"\NUL\NUL\NUL\NUL\NUL"

writeFile :: FilePath -> String -> IO () Source

The computation writeFile file str function writes the string str, to the file file.

This operation may fail with the same errors as hPutStr and withFile.

Examples
Expand
>>> writeFile "hello" "world" >> readFile "hello"
"world"
>>> writeFile "~/" "D:"
*** Exception: ~/: withFile: inappropriate type (Is a directory)

appendFile :: FilePath -> String -> IO () Source

The computation appendFile file str function appends the string str, to the file file.

Note that writeFile and appendFile write a literal string to a file. To write a value of any printable type, as with print, use the show function to convert the value to a string first.

This operation may fail with the same errors as hPutStr and withFile.

Examples
Expand

The following example could be more efficently written by acquiring a handle instead with openFile and using the computations capable of writing to handles such as hPutStr.

>>> let fn = "hello_world"
>>> in writeFile fn "hello" >> appendFile fn " world!" >> (readFile fn >>= putStrLn)
"hello world!"
>>> let fn = "foo"; output = readFile' fn >>= putStrLn
>>> in output >> appendFile fn (show [1,2,3]) >> output
this is what's in the file
this is what's in the file[1,2,3]

readIO :: Read a => String -> IO a Source

The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.

This operation may fail with:

Examples
Expand
>>> fmap (+ 1) (readIO "1")
2
>>> readIO "not quite ()" :: IO ()
*** Exception: user error (Prelude.readIO: no parse)

readLn :: Read a => IO a Source

The readLn function combines getLine and readIO.

This operation may fail with the same errors as getLine and readIO.

Examples
Expand
>>> fmap (+ 5) readLn
> 25
30
>>> readLn :: IO String
> this is not a string literal
*** Exception: user error (Prelude.readIO: no parse)

Exception handling in the I/O monad

type IOError = IOException Source

The Haskell 2010 type for exceptions in the IO monad. Any I/O operation may raise an IOError instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Exception.

In Haskell 2010, this is an opaque type.

ioError :: HasCallStack => IOError -> IO a Source

Raise an IOError in the IO monad.

userError :: String -> IOError Source

Construct an IOError value with a string describing the error. The fail method of the IO instance of the Monad class raises a userError, thus:

instance Monad IO where
  ...
  fail s = ioError (userError s)

The equality types

class a ~# b => (a :: k) ~ (b :: k) infix 4 Source

Lifted, homogeneous equality. By lifted, we mean that it can be bogus (deferred type error). By homogeneous, the two types a and b must have the same kinds.

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.12.1/docs/libraries/base-4.21.0.0-8e62/Prelude.html